Dongshuai Liu, Yanxia Gao, Dianyuan Fan, Boris A. Malomed, Lifu Zhang
Quantum droplets (QDs) are self-trapped modes stabilized by the Lee-Huang-Yang correction to the mean-field Hamiltonian of binary atomic Bose-Einstein condensates. The existence and stability of quiescent and rotating dipole-shaped and vortex QDs with vorticity $S=1$ (DQDs and VQDs, respectively) are numerically studied in the framework of the accordingly modified two-component system. The rotating DQDs trapped in an annular potential are built of two crescent-like components, stretching along the azimuthal direction with the increase of the rotation frequency. Rotating quadrupole QDs (QQDs) bifurcate from the VQDs with $S=2$. Above a certain rotation frequency, they transform back into VQDs with a flat-top shape. Rotating DQDs and QQDs are stable in a broad interval of values of the chemical potential. The results provide the first example of stable modes which are intermediate states between the rotating DQDs and QQDs on the one hand, and VQDs on the other.
{"title":"Rotating dipole and quadrupole quantum droplets in binary Bose-Einstein condensates","authors":"Dongshuai Liu, Yanxia Gao, Dianyuan Fan, Boris A. Malomed, Lifu Zhang","doi":"arxiv-2407.09129","DOIUrl":"https://doi.org/arxiv-2407.09129","url":null,"abstract":"Quantum droplets (QDs) are self-trapped modes stabilized by the\u0000Lee-Huang-Yang correction to the mean-field Hamiltonian of binary atomic\u0000Bose-Einstein condensates. The existence and stability of quiescent and\u0000rotating dipole-shaped and vortex QDs with vorticity $S=1$ (DQDs and VQDs,\u0000respectively) are numerically studied in the framework of the accordingly\u0000modified two-component system. The rotating DQDs trapped in an annular\u0000potential are built of two crescent-like components, stretching along the\u0000azimuthal direction with the increase of the rotation frequency. Rotating\u0000quadrupole QDs (QQDs) bifurcate from the VQDs with $S=2$. Above a certain\u0000rotation frequency, they transform back into VQDs with a flat-top shape.\u0000Rotating DQDs and QQDs are stable in a broad interval of values of the chemical\u0000potential. The results provide the first example of stable modes which are\u0000intermediate states between the rotating DQDs and QQDs on the one hand, and\u0000VQDs on the other.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"37 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719069","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sherzod R. Otajonov, Bakhram A. Umarov, Fatkhulla Kh. Abdullaev
The properties of quasi-one-dimensional quantum droplets of Bose-Einstein condensates are investigated analytically and numerically, taking into account the contribution of quantum fluctuations. Through the development of a variational approach employing the super-Gaussian function, we identify stationary parameters for the quantum droplets. The frequency of breathing mode oscillations in these quantum droplets is estimated. Moreover, the study reveals that periodic modulation in time of the atomic scattering length induces resonance oscillations in quantum droplet parameters or the emission of linear waves, contingent on the amplitude of the external modulation. A similar analysis is conducted for the Lee-Huang-Yang fluid, confined in a parabolic potential. Theoretical predictions are corroborated through direct numerical simulations of the governing extended Gross-Pitaevskii equation. Additionally, we study the collision dynamics of quasi-one-dimensional quantum droplets.
{"title":"Dynamics of quasi-one-dimensional quantum droplets in Bose-Bose mixtures","authors":"Sherzod R. Otajonov, Bakhram A. Umarov, Fatkhulla Kh. Abdullaev","doi":"arxiv-2407.07384","DOIUrl":"https://doi.org/arxiv-2407.07384","url":null,"abstract":"The properties of quasi-one-dimensional quantum droplets of Bose-Einstein\u0000condensates are investigated analytically and numerically, taking into account\u0000the contribution of quantum fluctuations. Through the development of a\u0000variational approach employing the super-Gaussian function, we identify\u0000stationary parameters for the quantum droplets. The frequency of breathing mode\u0000oscillations in these quantum droplets is estimated. Moreover, the study\u0000reveals that periodic modulation in time of the atomic scattering length\u0000induces resonance oscillations in quantum droplet parameters or the emission of\u0000linear waves, contingent on the amplitude of the external modulation. A similar\u0000analysis is conducted for the Lee-Huang-Yang fluid, confined in a parabolic\u0000potential. Theoretical predictions are corroborated through direct numerical\u0000simulations of the governing extended Gross-Pitaevskii equation. Additionally,\u0000we study the collision dynamics of quasi-one-dimensional quantum droplets.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"2018 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141584717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thulasidharan K., Sinthuja N., Vishnu Priya N., Senthilvelan M
We introduce a novel neural network structure called Strongly Constrained Theory-Guided Neural Network (SCTgNN), to investigate the behaviours of the localized solutions of the generalized nonlinear Schr"{o}dinger (NLS) equation. This equation comprises four physically significant nonlinear evolution equations, namely, (i) NLS equation, Hirota equation Lakshmanan-Porsezian-Daniel (LPD) equation and fifth-order NLS equation. The generalized NLS equation demonstrates nonlinear effects up to quintic order, indicating rich and complex dynamics in various fields of physics. By combining concepts from the Physics-Informed Neural Network (PINN) and Theory-Guided Neural Network (TgNN) models, SCTgNN aims to enhance our understanding of complex phenomena, particularly within nonlinear systems that defy conventional patterns. To begin, we employ the TgNN method to predict the behaviours of localized waves, including solitons, rogue waves, and breathers, within the generalized NLS equation. We then use SCTgNN to predict the aforementioned localized solutions and calculate the mean square errors in both SCTgNN and TgNN in predicting these three localized solutions. Our findings reveal that both models excel in understanding complex behaviours and provide predictions across a wide variety of situations.
{"title":"On examining the predictive capabilities of two variants of PINN in validating localised wave solutions in the generalized nonlinear Schrödinger equation","authors":"Thulasidharan K., Sinthuja N., Vishnu Priya N., Senthilvelan M","doi":"arxiv-2407.07415","DOIUrl":"https://doi.org/arxiv-2407.07415","url":null,"abstract":"We introduce a novel neural network structure called Strongly Constrained\u0000Theory-Guided Neural Network (SCTgNN), to investigate the behaviours of the\u0000localized solutions of the generalized nonlinear Schr\"{o}dinger (NLS)\u0000equation. This equation comprises four physically significant nonlinear\u0000evolution equations, namely, (i) NLS equation, Hirota equation\u0000Lakshmanan-Porsezian-Daniel (LPD) equation and fifth-order NLS equation. The\u0000generalized NLS equation demonstrates nonlinear effects up to quintic order,\u0000indicating rich and complex dynamics in various fields of physics. By combining\u0000concepts from the Physics-Informed Neural Network (PINN) and Theory-Guided\u0000Neural Network (TgNN) models, SCTgNN aims to enhance our understanding of\u0000complex phenomena, particularly within nonlinear systems that defy conventional\u0000patterns. To begin, we employ the TgNN method to predict the behaviours of\u0000localized waves, including solitons, rogue waves, and breathers, within the\u0000generalized NLS equation. We then use SCTgNN to predict the aforementioned\u0000localized solutions and calculate the mean square errors in both SCTgNN and\u0000TgNN in predicting these three localized solutions. Our findings reveal that\u0000both models excel in understanding complex behaviours and provide predictions\u0000across a wide variety of situations.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141584716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The instability of the Ivancevic option pricing model is studied through the variational method. We have analytically derived the dispersion relation of the IOPM for both constant volatility and Landau coefficient model and time-dependent volatility and Landau coefficient model. Also the IOPM was studies numerically using the 4th order Runge-Kutta method.
{"title":"Ivancevic Option Pricing Model modulational instability through the variational approach","authors":"Christopher Gaafele","doi":"arxiv-2407.12054","DOIUrl":"https://doi.org/arxiv-2407.12054","url":null,"abstract":"The instability of the Ivancevic option pricing model is studied through the\u0000variational method. We have analytically derived the dispersion relation of the\u0000IOPM for both constant volatility and Landau coefficient model and\u0000time-dependent volatility and Landau coefficient model. Also the IOPM was\u0000studies numerically using the 4th order Runge-Kutta method.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141740143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yuta Tateyama, Hiroaki Ito, Shigeyuki Komura, Hiroyuki Kitahata
We investigate the pattern dynamics of the one-dimensional non-reciprocal Swift-Hohenberg model. Characteristic spatiotemporal patterns, such as disordered, aligned, swap, chiral-swap, and chiral phases, emerge depending on the parameters. We classify the characteristic spatiotemporal patterns obtained in the numerical simulations by focusing on the spatiotemporal Fourier spectrum of the order parameters. We derive a reduced dynamical system by using the spatial Fourier series expansion. We analyze the bifurcation structure around the fixed points corresponding to the aligned and chiral phases and explain the transitions between them. The disordered phase is destabilized either to the aligned phase or to the chiral phase by the Turing bifurcation or the wave bifurcation, and the aligned phase and the chiral phase are connected by the pitchfork bifurcation.
{"title":"Pattern dynamics of the non-reciprocal Swift-Hohenberg model","authors":"Yuta Tateyama, Hiroaki Ito, Shigeyuki Komura, Hiroyuki Kitahata","doi":"arxiv-2407.05742","DOIUrl":"https://doi.org/arxiv-2407.05742","url":null,"abstract":"We investigate the pattern dynamics of the one-dimensional non-reciprocal\u0000Swift-Hohenberg model. Characteristic spatiotemporal patterns, such as\u0000disordered, aligned, swap, chiral-swap, and chiral phases, emerge depending on\u0000the parameters. We classify the characteristic spatiotemporal patterns obtained\u0000in the numerical simulations by focusing on the spatiotemporal Fourier spectrum\u0000of the order parameters. We derive a reduced dynamical system by using the\u0000spatial Fourier series expansion. We analyze the bifurcation structure around\u0000the fixed points corresponding to the aligned and chiral phases and explain the\u0000transitions between them. The disordered phase is destabilized either to the\u0000aligned phase or to the chiral phase by the Turing bifurcation or the wave\u0000bifurcation, and the aligned phase and the chiral phase are connected by the\u0000pitchfork bifurcation.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"49 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568756","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the fractional three-dimensional (3D) nonlinear Schr"{o}dinger equation with exponential saturating nonlinearity. In the case of the L'{e}vy index $alpha=1.9$, this equation can be considered as a model equation to describe strong Langmuir plasma turbulence. The modulation instability of a plane wave is studied, the regions of instability depending on the L'{e}vy index, and the corresponding instability growth rates are determined. Numerical solutions in the form of 3D fundamental soliton (ground state) are obtained for different values of the L'{e}vy index. It was shown that in a certain range of soliton parameters it is stable even in the presence of a sufficiently strong initial random disturbance, and the self-cleaning of the soliton from such initial noise was demonstrated.
{"title":"Three-dimensional solitons in fractional nonlinear Schrödinger equation with exponential saturating nonlinearity","authors":"Volodymyr M. Lashkin, Oleg K. Cheremnykh","doi":"arxiv-2407.05354","DOIUrl":"https://doi.org/arxiv-2407.05354","url":null,"abstract":"We study the fractional three-dimensional (3D) nonlinear Schr\"{o}dinger\u0000equation with exponential saturating nonlinearity. In the case of the L'{e}vy\u0000index $alpha=1.9$, this equation can be considered as a model equation to\u0000describe strong Langmuir plasma turbulence. The modulation instability of a\u0000plane wave is studied, the regions of instability depending on the L'{e}vy\u0000index, and the corresponding instability growth rates are determined. Numerical\u0000solutions in the form of 3D fundamental soliton (ground state) are obtained for\u0000different values of the L'{e}vy index. It was shown that in a certain range of\u0000soliton parameters it is stable even in the presence of a sufficiently strong\u0000initial random disturbance, and the self-cleaning of the soliton from such\u0000initial noise was demonstrated.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"8 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568755","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We introduce the notion of asymptotic integrability into the theory of nonlinear wave equations. It means that the Hamiltonian structure of equations describing propagation of high-frequency wave packets is preserved by hydrodynamic evolution of the large-scale background wave, so that these equations have an additional integral of motion. This condition is expressed mathematically as a system of equations for the carrier wave number as a function of the background variables. We show that a solution of this system for a given dispersion relation of linear waves is related with the quasiclassical limit of the Lax pair for the completely integrable equation having the corresponding dispersionless and linear dispersive behavior. We illustrate the theory by several examples.
{"title":"Asymptotic integrability of nonlinear wave equations","authors":"A. M. Kamchatnov","doi":"arxiv-2407.04244","DOIUrl":"https://doi.org/arxiv-2407.04244","url":null,"abstract":"We introduce the notion of asymptotic integrability into the theory of\u0000nonlinear wave equations. It means that the Hamiltonian structure of equations\u0000describing propagation of high-frequency wave packets is preserved by\u0000hydrodynamic evolution of the large-scale background wave, so that these\u0000equations have an additional integral of motion. This condition is expressed\u0000mathematically as a system of equations for the carrier wave number as a\u0000function of the background variables. We show that a solution of this system\u0000for a given dispersion relation of linear waves is related with the\u0000quasiclassical limit of the Lax pair for the completely integrable equation\u0000having the corresponding dispersionless and linear dispersive behavior. We\u0000illustrate the theory by several examples.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We employ weakly nonlinear theory to derive an amplitude equation for the conserved-Hopf instability, i.e., a generic large-scale oscillatory instability for systems with two conservation laws. The resulting equation represents the equivalent in the conserved case of the complex Ginzburg-Landau equation obtained in the nonconserved case as amplitude equation for the standard Hopf bifurcation. Considering first the case of a relatively simple symmetric Cahn-Hilliard model with purely nonreciprocal coupling, we derive the nonlinear nonlocal amplitude equation and show that its bifurcation diagram and time evolution well agree with results for the full model. The solutions of the amplitude equation and their stability are obtained analytically thereby showing that in oscillatory phase separation the suppression of coarsening is universal. Second, we lift the restrictions and obtain the amplitude equation in a more generic case, that also shows very good agreement with the full model as exemplified for some transient dynamics that converges to traveling wave states.
{"title":"An amplitude equation for the conserved-Hopf bifurcation -- derivation, analysis and assessment","authors":"Daniel Greve, Uwe Thiele","doi":"arxiv-2407.03670","DOIUrl":"https://doi.org/arxiv-2407.03670","url":null,"abstract":"We employ weakly nonlinear theory to derive an amplitude equation for the\u0000conserved-Hopf instability, i.e., a generic large-scale oscillatory instability\u0000for systems with two conservation laws. The resulting equation represents the\u0000equivalent in the conserved case of the complex Ginzburg-Landau equation\u0000obtained in the nonconserved case as amplitude equation for the standard Hopf\u0000bifurcation. Considering first the case of a relatively simple symmetric Cahn-Hilliard\u0000model with purely nonreciprocal coupling, we derive the nonlinear nonlocal\u0000amplitude equation and show that its bifurcation diagram and time evolution\u0000well agree with results for the full model. The solutions of the amplitude\u0000equation and their stability are obtained analytically thereby showing that in\u0000oscillatory phase separation the suppression of coarsening is universal.\u0000Second, we lift the restrictions and obtain the amplitude equation in a more\u0000generic case, that also shows very good agreement with the full model as\u0000exemplified for some transient dynamics that converges to traveling wave\u0000states.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The nonequilibrium dynamics of a cycling three state Potts model is studied on a square lattice using Monte Carlo simulations and continuum theory. This model is relevant to chemical reactions on a catalytic surface and to molecular transport across a membrane. Several characteristic modes are formed depending on the flipping energies between successive states and the contact energies between neighboring sites. Under cyclic symmetry conditions, cycling homogeneous phases and spiral waves form at low and high flipping energies, respectively. In the intermediate flipping energy regime, these two modes coexist temporally in small systems and/or at low contact energies. Under asymmetric conditions, we observed small biphasic domains exhibiting amoeba-like locomotion and temporal coexistence of spiral waves and a dominant non-cyclic one-state phase. An increase in the flipping energy between two successive states, say state 0 and state 1, while keeping the other flipping energies constant, induces the formation of the third phase (state 2), owing to the suppression of the nucleation of state 0 domains. Under asymmetric conditions regarding the contact energies, two different modes can appear depending on the initial state, due to a hysteresis phenomenon.
{"title":"Spatiotemporal patterns in the active cyclic Potts model","authors":"Hiroshi Noguchi, Jean-Baptiste Fournier","doi":"arxiv-2407.02985","DOIUrl":"https://doi.org/arxiv-2407.02985","url":null,"abstract":"The nonequilibrium dynamics of a cycling three state Potts model is studied\u0000on a square lattice using Monte Carlo simulations and continuum theory. This\u0000model is relevant to chemical reactions on a catalytic surface and to molecular\u0000transport across a membrane. Several characteristic modes are formed depending\u0000on the flipping energies between successive states and the contact energies\u0000between neighboring sites. Under cyclic symmetry conditions, cycling\u0000homogeneous phases and spiral waves form at low and high flipping energies,\u0000respectively. In the intermediate flipping energy regime, these two modes\u0000coexist temporally in small systems and/or at low contact energies. Under\u0000asymmetric conditions, we observed small biphasic domains exhibiting\u0000amoeba-like locomotion and temporal coexistence of spiral waves and a dominant\u0000non-cyclic one-state phase. An increase in the flipping energy between two\u0000successive states, say state 0 and state 1, while keeping the other flipping\u0000energies constant, induces the formation of the third phase (state 2), owing to\u0000the suppression of the nucleation of state 0 domains. Under asymmetric\u0000conditions regarding the contact energies, two different modes can appear\u0000depending on the initial state, due to a hysteresis phenomenon.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"34 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Loic Fache, Hervé Damart, François Copie, Thibault Bonnemain, Thibault Congy, Giacomo Roberti, Pierre Suret, Gennady El, Stéphane Randoux
We present an experimental study on the perturbed evolution of Korteweg-deVries soliton gases in a weakly dissipative nonlinear electrical transmission line. The system's dynamics reveal that an initially dense, fully randomized, soliton gas evolves into a coherent macroscopic state identified as a soliton condensate through nonlinear spectral analysis. The emergence of the soliton condensate is driven by the spatial rearrangement of the systems's eigenmodes and by the proliferation of new solitonic states due to nonadiabatic effects, a phenomenon not accounted for by the existing hydrodynamic theories.
{"title":"Dissipation-driven emergence of a soliton condensate in a nonlinear electrical transmission line","authors":"Loic Fache, Hervé Damart, François Copie, Thibault Bonnemain, Thibault Congy, Giacomo Roberti, Pierre Suret, Gennady El, Stéphane Randoux","doi":"arxiv-2407.02874","DOIUrl":"https://doi.org/arxiv-2407.02874","url":null,"abstract":"We present an experimental study on the perturbed evolution of\u0000Korteweg-deVries soliton gases in a weakly dissipative nonlinear electrical\u0000transmission line. The system's dynamics reveal that an initially dense, fully\u0000randomized, soliton gas evolves into a coherent macroscopic state identified as\u0000a soliton condensate through nonlinear spectral analysis. The emergence of the\u0000soliton condensate is driven by the spatial rearrangement of the systems's\u0000eigenmodes and by the proliferation of new solitonic states due to nonadiabatic\u0000effects, a phenomenon not accounted for by the existing hydrodynamic theories.","PeriodicalId":501370,"journal":{"name":"arXiv - PHYS - Pattern Formation and Solitons","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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