# gst: the hypothesis of a new type of rogue waves.

<< Much attention of researchers has been paid in the recent decades to the study of rogue waves. Various mechanisms of formation of these waves were suggested. The occurrence of rogue waves is most often investigated on the basis of the mechanisms of modulation instability and superposition of waves. In both cases, an evolution of rogue waves takes place against the background of a wave field, which is reflected in the definitions of such waves. In this report, the localized waves developed in the absence of the background wave fields are considered. At the same time, their dynamics corresponds to the dynamics of rogue waves that ”appear from nowhere and disappear without a trace”. >>️

<< The waves of this type are distinguished by the fact that their dynamics occur on the zero background. This implies that rogue waves presented here are formed solely due to the nonlinear focusing. >>️

N.V. Ustinov. New type of rogue waves. arXiv:2310.17254v1 [nlin.SI]. Oct 26, 2023.  

https://arxiv.org/abs/2310.17254

Chaos, Solitons & Fractals V. 179, Feb 2024, 114467. https://www.sciencedirect.com/science/article/abs/pii/S0960077924000183

Also: waves, in https://www.inkgmr.net/kwrds.html

Keywords: gst, waves, rogue waves 

# gst: mitigate | eliminate side lobes from superoscillatory waves (to manipulate nanoparticles)

<< A sharp-edged aperture is a promising solution for eliminating side lobes from superoscillatory waves. >>

<< Optical superoscillation refers to a wave packet that can oscillate locally in a frequency exceeding its highest Fourier component. This intriguing phenomenon enables production of extremely localized waves that can break the optical diffraction barrier. >>

<< The trouble is that strong side lobes accompany the main lobes of superoscillatory waves, which limits the field of view and hinders application. >>️

<< A central microdisc with cylindrical diffraction gives rise to a superoscillatory light spot of a size within the optical diffraction limit. A pair of sharp-edged apertures ensures constructive interference with the high-spatial-frequency waves. That interference effectively eliminates side lobes along a symmetric cut that can be adjusted in the transverse plane by rotating the moonlike apertures. >>

️

<< the cylindrical diffraction of the central microdisc produces superoscillatory waves with Bessel-like forms. These forms enable the delicate structures of the superoscillatory waves propagating in free space to travel much farther than the evanescent light waves. (..) this intriguing propagation effect of superoscillation holds promise for potential application in nanoparticle manipulation, as well as superresolution imaging. >>️

️

Optical superoscillation without side waves. SPIE-International Society for Optics and Photonics. Jun 24, 2021.

https://www.sciencedaily.com/releases/2021/06/210624170837.htm

Yanwen Hu, Shiwang Wang, et al. Optical superoscillatory waves without side lobes along a symmetric cut. Advanced Photonics, 3(4), 045002 doi: 10.1117/ 1.AP.3.4.045002. Jun 23, 2021. 

https://www.spiedigitallibrary.org/journals/advanced-photonics/volume-3/issue-4/045002/Optical-superoscillatory-waves-without-side-lobes-along-a-symmetric-cut/10.1117/1.AP.3.4.045002.full

# gst: fluid stretching and compression to control (chemical) waves

<< Oscillatory kinetics coupled to diffusion can produce traveling waves as observed in physical, chemical, and biological systems. (AA) show experimentally that the properties of such waves can be controlled by fluid stretching and compression in a hyperbolic flow. >>

️

<< Localized packet waves consisting in a train of parallel waves can develop due to a balance between diffusive broadening and advective compression along the unstable manifold. At a given distance from the stagnation point, the parallel waves transform into planelike waves and smeared waves where the transverse parabolic flow profile disturbs the patterns in the gap width. >> 

<< Once a wave packet has been obtained, it imprints a privileged direction that is maintained even if the compression rate is decreased. The width of the wave packet then scales inversely with the compression rate. >>️

S. Izumoto, D. M. Escala, et al. Control of Chemical Waves by Fluid Stretching and Compression. Phys. Rev. Lett. 133, 218001. Nov 21, 2024. 

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.133.218001

Also: waves, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves

# gst: apropos of transitions, tsunami waves generated by granular collapses.

<< Tsunami waves induced by landslides are a threat to human activities and safety along coastal areas. In this paper, (AA) characterize experimentally the waves generated by the gravity-driven collapse of a dry granular column into water. Three nonlinear wave regimes are identified depending on the Froude number Fr_f based on the ratio of the velocity of the advancing granular front and the velocity of linear gravity waves in shallow water: transient bores for large Fr_f, solitary waves for intermediate values of Fr_f, and nonlinear transition waves at small Fr_f. >>️

Wladimir Sarlin, Cyprien Morize, et al. Nonlinear regimes of tsunami waves generated by a granular collapse.    

Journal of Fluid Mechanics, 919, R6. doi:10.1017/ jfm.2021.400. May 28, 2021. 

https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/abs/nonlinear-regimes-of-tsunami-waves-generated-by-a-granular-collapse/3F38B26548B891FA9AE8A4018FF992A4#

James Badham. The Science of tsunamis. University of California. Santa Barbara. Jun 21, 2021. 

https://www.sciencedaily.com/releases/2021/06/210621160524.htm

Froude number (Fr_f)

https://en.m.wikipedia.org/wiki/Froude_number

Also

keyword 'grain' in FonT

https://flashontrack.blogspot.com/search?q=grain

keyword 'grani' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=grani

keyword 'waves' in FonT

https://flashontrack.blogspot.com/search?q=waves

keyword 'onda' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=onda

# gst: spiral defect chaos with intermittency increases mean termination time

<< ️Cardiac models are examples of excitable systems and can support stable spiral waves. For certain parameter values, however, these spiral waves can become unstable, resulting in spiral defect chaos (SDC), characterized by the continuous creation and annihilation of spiral waves and thought to underlie atrial fibrillation. During SDC, the number of spiral waves fluctuates and drops to zero at termination. >>

<< ️In this work, (AA) demonstrate that varying a single parameter allows the system to transition from SDC to a single spiral wave, passing through an intermediate regime of intermittency. In such intermittent dynamics, intervals of SDC are sandwiched between non-SDC intervals during which the number of spiral waves remains small and constant. (They) quantify this intermittency and show that the mean termination time increases significantly as the control parameter approaches values for which a single spiral wave is stable. >>

<<  In addition, (AA) observe that quasistable spiral waves may intermittently persist in part of the computational domain, while the rest of the domain exhibits SDC. >> 

Mahesh Kumar Mulimani, Wouter-Jan Rappel. Spiral defect chaos with intermittency increases mean termination time. Phys. Rev. E 112, 034203. Sep 3, 2025.

https://journals.aps.org/pre/abstract/10.1103/bwpl-qqyl

arXiv: 2505.06427v1 [nlin.CD]. May 9,  2025

https://arxiv.org/abs/2505.06427

Also: waves, intermittency, vortex, chaos, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, spiral & scroll waves, intermittency, vortex, chaos, spiral defect chaos.

# s-gst: subtle, interacting internal waves

<< This  photograph,  taken  from  the  International  Space  Station  (ISS),  shows  the  north  coast  of  Trinidad  and  a  series  of  subtle, interacting  arcs  in  the  southeastern  Caribbean  Sea.  These  are  known  as  “internal  waves,”  the  surface  manifestation  of  slow waves  that  move  tens  of  meters  beneath  the  sea  surface.  Internal  waves  produce  enough  of  an  effect  on  the  sea  surface  to be  seen  from  space,  but  only  where  they  are  enhanced  due  to  reflection  of  sunlight,  or  sunglint,  back  towards  the  International Space  Station. The  image  shows  at  least  three  sets  of  internal  waves  interacting.  The  most  prominent  set  (image  top  left)  shows  a  packet  of several  waves  moving  from  the  northwest  due  to  the  tidal  flow  towards  the  north  coast  of  Trinidad.  Two  less  prominent, younger  sets  can  be  seen  further  out  to  sea.  A  very  broad  set  enters  the  view  from  the  north  and  northeast,  and  interacts  at image  top  center  with  the  first  set.  All  the  internal  waves  are  probably  caused  by  the  shelf  break  near  Tobago  (outside  the image  to  top  right).  The  shelf  break  is  the  step  between  shallow  seas  (around  continents  and  islands)  and  the  deep  ocean.  It is  the  line  at  which  tides  usually  start  to  generate  internal  waves. >>

NASA Earth Observatory.  Internal Waves off Northern Trinidad. February 4, 2013

http://m.earthobservatory.nasa.gov/IOTD/view.php?id=80337

image: download  large  image  (391  KB,  JPEG,  1440x960)

http://eoimages.gsfc.nasa.gov/images/imagerecords/80000/80337/ISS034-E-032377_lrg.jpg

# gst: exploring the on-demand dynamical generation of a plethora of dispersive shock waves arising in attractive one-dimensional droplet-bearing environment.

AA << demonstrate the controllable generation of distinct types of dispersive shock-waves emerging in a quantum droplet bearing environment with the aid of step-like initial conditions. Dispersive regularization of the ensuing hydrodynamic singularities occurs due to the competition between meanfield repulsion and attractive quantum fluctuations. This interplay delineates the dominance of defocusing (hyperbolic) and focusing (elliptic) hydrodynamic phenomena respectively being designated by real and imaginary speed of sound. >>

<< Surprisingly, dispersive shock waves persist across the hyperbolic-to-elliptic threshold, while a plethora of additional wave patterns arise, such as rarefaction waves, traveling dispersive shock waves, (anti)kinks and droplet wavetrains. >>

AA << results pave the way for unveiling a multitude of unexplored coherently propagating waveforms in such attractively interacting mixtures. >>

Sathyanarayanan Chandramouli, Simeon I. Mistakidis, Garyfallia C. Katsimiga, Panayotis G. Kevrekidis. 

Dispersive shock waves in a one-dimensional droplet-bearing environment. arXiv: 2404.02998v2 [nlin.PS]. Apr 5, 2024. 

https://arxiv.org/abs/2404.02998

Also: waves, drop, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, drops 

# gst: spontaneous emergence of solitary waves in active flow networks.

<< ️Flow networks are fundamental for understanding systems such as animal and plant vasculature or power distribution grids. These networks can encode, transmit, and transform information embodied in the spatial and temporal distribution of their flows. >>

<< ️In this work, (AA) focus on a minimal yet physically grounded system that allows (Them) to isolate the fundamental mechanisms by which active flow networks generate and regulate emergent dynamics capable of supporting information transmission. The system is composed of active units that pump fluid and elastic units that store volume. From first principles, (They) derive a discrete model-an active flow network-that enables the simulation of large systems with many interacting units. >>

<< ️Numerically, (AA) show that the pressure field can develop solitary waves, resulting in the spontaneous creation and transmission of localized packets of information stored in the physical properties of the flow. (They) characterize how these solitary waves emerge from disordered initial conditions in a one-dimensional network, and how their size and propagation speed depend on key system parameters. >>

<< ️Finally, when the elastic units are coupled to their neighbors, the solitary waves exhibit even richer dynamics, with diverse shapes and finite lifetimes that display power-law behaviors that (They) can predict analytically. >>

Rodrigo Fernández-Quevedo García, Gonçalo Cruz Antunes, Jens Harting, et al. Spontaneous emergence of solitary waves in active flow networks. arXiv: 2511.13448v1 [physics.flu-dyn]. Nov 17, 2025.

https://arxiv.org/abs/2511.13448

Also: soliton, waves, network, elastic, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, solitons, waves, solitary waves, networks, active flow networks, active matter, fluid-structure interactions, elasticity.

# gst: apropos of transitions: effects of random waves interacting with a coherent structure

<< Solitary waves interacting with random (..) waves (..) are studied. Two opposing types of dynamics are identified: First, the random thermal waves can erode the solitary wave; second, this structure can grow as a result of this interaction. These two types of behavior depend on a dynamical property of the solitary wave (its angular frequency), and on a statistical property of the thermal waves (the chemical potential). >>

<< Either process leads to an increase of the wave entropy. >>

Yuanting Chen, Benno Rumpf. Growth or decay of a coherent structure interacting with random waves. Phys. Rev. E 104, 034213. Sep 15, 2021.

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.104.034213

Also

keyword 'waves' in FonT

https://flashontrack.blogspot.com/search?q=waves

keyword 'onda' in Notes (quasi-stochastic poetry)

https://inkpi.blogspot.com/search?q=onda

# gst: nascent water waves induced by the impulsive motion of a solid wall; an unsteady hydraulic jump theory

Fig. 2: Representative cases of the different regimes of impulse waves observed: (a) dispersive wave; (b) solitary-like wave; (c) plunging breaking bore; (d) water jet 

AA << investigated the generation phase of laboratory-scale water waves induced by the impulsive motion of a rigid piston, whose maximum velocity U and total stroke L are independently varied, as well as the initial liquid depth h. By doing so, the influence of two dimensionless numbers is studied: the Froude number Frp (..), with g the gravitational acceleration, and the relative stroke Λp (..) of the piston. >>️

<< For large Froude numbers, an unsteady hydraulic jump theory is proposed, which accurately predicts the time evolution of the wave amplitude at the contact with the piston throughout the generation phase. At the end of the formation process, the dimensionless volume of the bump evolves linearly with Λp and the wave aspect ratio is found to be governed by the relative acceleration γ/g. As the piston begins its constant deceleration, the water bump evolves into a propagating wave and several regimes (such as dispersive, solitary-like and bore waves, as well as water jets) are then reported and mapped in a phase diagram in the (Frp, Λp) plane. While the transition from waves to water jets is observed if the typical acceleration of the piston is close enough to the gravitational acceleration g, the wave regimes are found to be mainly selected by the relative piston stroke Λp while the Froude number determines whether the generated wave breaks or not. >>️

️

Wladimir Sarlin, Zhaodong Niu, et al. Nascent water waves induced by the impulsive motion of a solid wall. arXiv: 2412.08216v1 [physics.flu-dyn]. Dec 11, 2024. 

https://arxiv.org/abs/2412.08216

Also: waves, soliton, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, soliton

# gst: chemical waves exhibit fascinating patterns

<< Waves are known in many very different forms; as water waves, light waves or sound waves. But here we are dealing with something quite different - chemical waves >>

<< Typically, one imagines a chemical reaction like this: from specific initial reactants one obtains specific final products. But it does not need to be as simple as that. Self-sustaining oscillations may occur, i.e. periodic changes between two different states >>

<< On a polycrystalline surface, there are then different regions in which the cyclical process occurs at different frequencies. It is precisely this effect that creates those fascinating wave patterns. When a chemical wave moves across the surface and passes from the edge of one grain of crystal to another, it speeds up or slows down, similar to light passing from the air to water.  This changes the complex spiral wave structures according to the particular orientation of the grain surface >>

Vienna University of Technology. Chemical waves guide to catalysts of the future. Feb 20, 2018.

https://m.phys.org/news/2018-02-chemical-catalysts-future.html

Yuri Suchorski, Martin Datler, et al. Visualizing catalyst heterogeneity by a multifrequential oscillating reaction. Nature Communication. 2018; 9 (600). doi: 10.1038/s41467-018-03007-3. Feb 9,  2018.

https://www.nature.com/articles/s41467-018-03007-3

# gst: bent and reverse bent solitons; obliquely interacting solitary waves and wave wakes in free-surface flows.

This AA paper << investigates the weakly nonlinear isotropic bi-directional Benney-Luke (BL) equation, which is used to describe oceanic surface and internal waves in shallow water, with a particular focus on soliton dynamics. Using the Whitham modulation theory, (AA) derive the modulation equations associated with the BL equation that describe the evolution of soliton amplitude and slope. By analyzing rarefaction waves and shock waves within these modulation equations, (AA) derive the Riemann invariants and modified Rankine-Hugoniot conditions. These expressions help characterize the Mach expansion and Mach reflection phenomena of bent and reverse bent solitons. >>

<< Furthermore, as a far-field approximation for the forced BL equation - which models wave and flow interactions with local topography - the modulation equations yield a slowly varying similarity solution. This solution indicates that the precursor wavefronts created by topography moving at subcritical or critical speeds take the shape of a circular arc, in contrast to the parabolic wavefronts observed in the forced KP equation. >>

Lei Hu, Xudan Luo, Zhan Wang. Obliquely interacting solitary waves and wave wakes in free-surface flows. arXiv: 2412.05034v1 [nlin.PS]. Dec 6, 2024. 

https://arxiv.org/abs/2412.05034

Also: waves, soliton, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, solitons

# gst: apropos of waves that escape trapping; on internal wave whispering gallery modes in channels and critical-slope wave attractors.

<< ️Internal waves are an important feature of stratified fluids, both in oceanic and lake basins and in other settings. Many works have been published on the generic feature of internal wave trapping onto planar wave attractors and super-attractors in 2D & 3D and the exceptional class of standing global internal wave modes. >>

<< ️However, most of these works did not deal with waves that escape trapping. By using continuous symmetries (AA) analytically prove the existence of internal wave Whispering Gallery Modes (WGMs), internal waves that propagate continuously without getting trapped by attractors. WGMs neutral stability with respect to different perturbations enable whispering gallery beams, a continuum of rays propagating together coherently. The systems' continuous symmetries also enable projection onto 2D planes that yield effective 2D billiards preserving the original dynamics. >>

<< ️By examining rays deviating from these WGMs in parabolic channels (They) discover a new type of wave attractor which is located along the channel instead of across it as in previous works. This new wave attractor leads to a re-understanding of WGMs as sitting at the border between the two basins of attraction. >>

<< ️Finally, both critical-slope wave attractors and whispering gallery beams are used to propose explanations for along-channel energy fluxes in submarine canyons and tidal energy intensification near critical slopes. >>

Nimrod Bratspiess, Eyal Heifetz, Leo R. M. Maas. On internal wave whispering gallery modes in channels and critical-slope wave attractors. arXiv: 2510.07218v1 [physics.flu-dyn]. Oct 8, 2025.

https://arxiv.org/abs/2510.07218

Also: waves, billiard, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, internal waves, internal wave whispering gallery modes (WGMs), wave attractors, basins of attraction, billiards.

# gst: shock waves in classical dust collapse.

<< ️During gravitational collapse of dust in spherical symmetry, matter particles may collide forming shell crossing singularities (SCSs) at which the Einstein equations become indeterminate. >>

<< ️(AA) show that in the case of marginally bound dust collapse, there is a unique evolution beyond SCSs such that a propagating shock wave forms, the metric remains continuous, and the stress-energy tensor dynamically becomes that of a thin shell. (They) give numerical simulations that exhibit this result. >>

Viqar Husain, Hassan Mehmood. Shock waves in classical dust collapse. Phys. Rev. Research 7, 033215. Sep 3, 2025.

https://journals.aps.org/prresearch/abstract/10.1103/b317-86qs

arXiv: 2504.14883v1 [gr-qc]. Apr 21, 2025.

https://arxiv.org/abs/2504.14883

Also: particle, singularity, collapse, waves, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, particles, singularity, shell crossing singularities, waves, shock waves, gravitational waves, collapse, dust collapse, gravitational collapse. 

# s-gst: vortex knots in wave systems

<< Waves  surround  us  all  the  time:  sound waves in  the  noise  around  us, light  waves enabling  us  to see,  and  according  to  quantum  mechanics,  all  matter  has  a  wave  nature.  Most  of  these  waves, however,  do  not  resemble  the  regular  train  of  waves  at  the  shore  of  the  ocean—the  pattern  is much  more  chaotic.  Most  significantly,  the  whirls  and  eddies  form  lines  in  space  called  vortices. Along  these  lines,  the  wave  intensity  is  zero,  and  natural  wave  fields  -  light,  sound  and  quantum matter  -  are  filled  with  a  dense  tangle  of  these  null  filaments >>

Knots  in  chaotic  waves. July  29,  2016.

http://m.phys.org/news/2016-07-chaotic.html

Alexander J. Taylor & Mark R. Dennis. Vortex knots in tangled quantum eigenfunctions. Nature Communications. Published 29 Jul 2016 DOI: 10.1038/ncomms12346 OPEN

http://www.nature.com/ncomms/2016/160729/ncomms12346/full/ncomms12346.html

# gst: scattered waves fuel emergent activity.

<< Active matter taps into external energy sources to power its own processes. Systems of passive particles ordinarily lack this capacity, but can become active if the constituent particles interact with each other nonreciprocally. By reformulating the theory of classical wave-matter interactions, (AA) demonstrate that interactions mediated by scattered waves generally are not constrained by Newton's third law. The resulting center-of-mass forces propel clusters of scatterers, enabling them to extract energy from the wave and rendering them active. This form of activity is an emergent property of the scatterers' state of organization and can arise in any system where mobile objects scatter waves. Emergent activity flips the script on conventional active matter whose nonreciprocity emerges from its activity, and not the other way around. >>

AA << combine theory, experiment, and simulation to illustrate how emergent activity arises in wave-matter composite systems and to explore the phenomenology of emergent activity in experimentally accessible models. These preliminary studies suggest that heterogeneity is a singular perturbation to the dynamics of wave-matter composite systems, and induces emergent activity under all but the most limited circumstances. >>️

Ella M. King, Mia C. Morrell, et al. Scattered waves fuel emergent activity. Phys. Rev. Research 7, 013055. Jan 15, 2025

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.7.013055

Also: waves, particle, self-assembly, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, particle, self-assembly

# geo: strange waves from Mayotte

<< On the morning of November 11, just before 9:30 UT, a mysterious rumble rolled around the world. The seismic waves began roughly 15 miles off the shores of Mayotte, a French island sandwiched between Africa and the northern tip of Madagascar. The waves buzzed across Africa, ringing sensors in Zambia, Kenya, and Ethiopia. They traversed vast oceans, humming across Chile, New Zealand, Canada, and even Hawaii nearly 11,000 miles away. >>

<< Yet many features of the waves are remarkably weird-from their surprisingly monotone, low-frequency “ring” to their global spread. >>

Maya Wei-Haas. Strange waves rippled around the world, and nobody knows why. Nov28, 2018.

https://www.nationalgeographic.com/science/2018/11/strange-earthquake-waves-rippled-around-world-earth-geology/

# gst: wave-kinetic dynamics of forced-dissipated turbulent internal gravity waves

<< Internal gravity waves are an essential feature of stratified media, such as oceans and atmospheres. >>

<< To investigate their dynamics, (AA) perform simulations of the forced-dissipated kinetic equation describing the evolution of the energy spectrum of weakly nonlinear internal gravity waves. >>

<< During the early evolution, three well-known nonlocal interactions, the elastic scattering, the induced diffusion, and the parametric subharmonic instability, together with a superharmonic resonance play a prominent role. >>

<< In contrast, local interactions are responsible for anisotropic energy cascade on longer timescales. >>

AA << reveal emergence of a condensate at small horizontal wave vectors that can be interpreted as a pure wave-wave interaction-mediated layering process. >>

Vincent Labarre, Giorgio Krstulovic, Sergey Nazarenko. Wave-Kinetic Dynamics of Forced-Dissipated Turbulent Internal Gravity Waves. Phys. Rev. Lett. 135, 014101. Jul 1, 2025.

https://journals.aps.org/prl/abstract/10.1103/b82h-z21n

arXiv:2407.11469v3 [physics.flu-dyn]. Mar 28, 2025.

https://arxiv.org/abs/2407.11469

Also: waves, weak, turbulence, transition, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, waves, weakness, turbulence, transitions, stratified turbulence, wave-turbulence interactions, weak turbulence.

# gst: the generation of solitary waves to move and direct a pulse-drive bot

<< The unique properties of nonlinear waves have been recently exploited to enable a wide range of applications, including impact mitigation, asymmetric transmission, switching, and focusing. (..) (AA) demonstrate that the propagation of nonlinear waves can be as well harnessed to make flexible structures crawl. By combining experimental and theoretical methods, (they) show that such pulse-driven locomotion reaches a maximum efficiency when the initiated pulses are solitons and that (their) simple machine can move on a wide range of surfaces and even steer. >>

<< nonlinear waves (..) demonstrates that they offer a new platform to make flexible machines to move. >>

Bolei Deng, Liyuan Chen, et al. Pulse-driven robot: Motion via solitary waves. Science Advances. Vol. 6, no. 18, eaaz1166. doi: 10.1126/ sciadv.aaz1166. May 1, 2020. 

https://advances.sciencemag.org/content/6/18/eaaz1166   

Pulse-driven robot: Motion via solitary waves. Thamarasee Jeewandara. May 8, 2020.

https://phys.org/news/2020-05-pulse-driven-robot-motion-solitary.html    

# gst: apropos of transitions, rich behaviors from chimeras or solitary states to traveling waves

AA << study numerically the spatiotemporal dynamics of a ring network of nonlocally coupled nonlinear oscillators, each represented by a two-dimensional discrete-time model of the classical van der Pol oscillator. >>

<< It is shown that the discretized oscillator exhibits a richer behavior, combining the peculiarities of both the original system and its own dynamics. Moreover, a large variety of spatiotemporal structures is observed in the network of discrete van der Pol oscillators when the discretization parameter and the coupling strength are varied. Such regimes as the coexistence of multichimera state/traveling wave and solitary state are revealed for the first time and studied in detail. >>

<< It is established that the majority of the observed chimera/solitary states, including the newly found ones, are transient towards the purely traveling wave mode. The peculiarities of the transition process and the lifetime (transient duration) of the chimera structures and the solitary state are analyzed depending on the system parameters, observation time, initial conditions, and influence of external noise. >>

Elena Rybalova, Sishu Muni, Galina Strelkova. Transition from chimera/solitary states to traveling waves. arXiv: 2212.07990v1 [nlin.AO]. Dec 15, 2022. 

https://arxiv.org/abs/2212.07990

Also

keyword 'transition' | 'transitional' in FonT

https://flashontrack.blogspot.com/search?q=transition

https://flashontrack.blogspot.com/search?q=transitional

keyword 'transition' | 'transizion*' in Notes (quasi-stochastic poetry)

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keyword 'waves' in FonT

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keyword 'onda' in Notes (quasi-stochastic poetry)

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Keywords: gst, behavior, van der Pol oscillator, transition, chimera state, solitons, solitary state, waves, noise