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Rational Waves and Complex Dynamics: Analytical Insights into a Generalized Nonlinear Schrödinger Equation with Distributed Coefficients

Sheng Zhang, Lijie Zhang, Bo Xu
2019 Complexity  
To illustrate the effectiveness of the complex multirational exp-function ansatz, we then consider a generalized nonlinear Schrödinger (gNLS) equation with distributed coefficients.  ...  Finally, we simulate some spatial structures and dynamical evolutions of the modules of the obtained solutions for more insights into these complex rational waves.  ...  In this paper, with a complex multirational exp-function ansatz, we shall construct and gain more insights into the rational solutions, including solitary wave solutions, N-wave solutions, and rouge wave  ... 
doi:10.1155/2019/3206503 fatcat:oz7i2cm4ava6log5tnu2o7t4um

Resonant Hamiltonian systems and weakly nonlinear dynamics in AdS spacetimes [article]

Oleg Evnin
2021 arXiv   pre-print
Schrodinger equations in harmonic potentials.  ...  Weakly nonlinear dynamics in anti-de Sitter (AdS) spacetimes is reviewed, keeping an eye on the AdS instability conjecture and focusing on the resonant approximation that accurately captures in a simplified  ...  G006918N, from Vrije Universiteit Brussel through the strategic research program High-Energy Physics, and from Polish National Science Centre through grant number 2017/26/A/ST2/00530.  ... 
arXiv:2104.09797v1 fatcat:6z7nepum4jdprdthbrrdxyok5e

Recent progress in investigating optical rogue waves

N Akhmediev, J M Dudley, D R Solli, S K Turitsyn
2013 Journal of Optics  
Yan and Dai [124] consider self-similar optical rogue wave solutions and interactions for the generalized higher-order nonlinear Schrödinger (HONLS) equation with space-and time-modulated parameters.  ...  He presents a similarity transformation to reduce the generalized HONLS equation to the higher-order integrable Hirota equation with constant coefficients.  ...  Yan and Dai [124] consider self-similar optical rogue wave solutions and interactions for the generalized higher-order nonlinear Schrödinger (HONLS) equation with space-and time-modulated parameters.  ... 
doi:10.1088/2040-8978/15/6/060201 fatcat:ojpqrvdxzjbm3hnuabyk62ul6u

Dynamical chaos of solitons and nonlinear periodic waves

F.Kh. Abdullaev
1989 Physics reports  
Spatial and temporal chaos in the sine-Gordon system 1.1. Direct methods of perturbation theory for solitons 6 3.4. Breather chaos in the nonlinear Schrodinger equation 1.2.  ...  Perturbation theory based on the inverse scattering with damping and amplification transform 9 3.5. Stochastic dynamics of a breather interacting with a 1.3.  ...  Acknowledgements The author is grateful to his colleagues for valuable discussions and criticism and expresses his appreciation to Drs. A.A. Abdumalikov, S.A. Darmanyan and B.A.  ... 
doi:10.1016/0370-1573(89)90098-7 fatcat:r23v64jpbbeebn35g3tqmb2cxi

Chirped Peregrine solitons in a class of cubic-quintic nonlinear Schrödinger equations

Shihua Chen, Fabio Baronio, Jose M. Soto-Crespo, Yi Liu, Philippe Grelu
2016 Physical review. E  
We shed light on the fundamental form of the Peregrine soliton as well as on its frequency chirping property by virtue of a pertinent cubic-quintic nonlinear Schrödinger equation.  ...  An exact generic Peregrine soliton solution is obtained via a simple gauge transformation, which unifies the recently-most-studied fundamental rogue-wave species.  ...  ACKNOWLEDGMENTS We thank André Mysyrowicz and Bernard Prade from LOA for helpful discussions.  ... 
doi:10.1103/physreve.93.062202 pmid:27415250 fatcat:mgjaugyyfza2lm5fsyahr46bhy

Dynamics of Nonlinear Waves on Bounded Domains [article]

Maciej Maliborski
2016 arXiv   pre-print
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution.  ...  The main body of this dissertation is concerned with construction (by means of perturbative and numerical methods) of time-periodic solutions for various nonlinear wave equations on bounded domains.  ...  Abstract This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution.  ... 
arXiv:1603.00935v1 fatcat:o3jiqo7y25cfnnphppc3vksnpq

Rogue Wave Modes for the Coupled Nonlinear Schrödinger System with Three Components: A Computational Study

Hiu Ning Chan, Kwok Wing Chow
2017 Applied Sciences  
This same computational approach can be adopted to study coupled nonlinear Schrödinger equations for the "non-integrable" regime, where the coefficients of self-phase modulation and cross-phase modulation  ...  The system of "integrable" coupled nonlinear Schrödinger equations (Manakov system) with three components in the defocusing regime is considered.  ...  Acknowledgments: Partial financial support for this project has been provided by the Research Grants Council contracts HKU711713E and HKU17200815.  ... 
doi:10.3390/app7060559 fatcat:tsxb47g5hrfvnmwvhekkbxhire

Complex-Dynamical Solution to the Many-Body Interaction Problem and Its Applications in Fundamental Physics [article]

Andrei P. Kirilyuk
2014 arXiv   pre-print
We review the recently proposed unreduced, complex-dynamical solution to the many-body problem with arbitrary interaction and its application to the unified solution of fundamental problems, including  ...  of the unified origin of quantum mechanics, relativity (special and general), elementary particles, their intrinsic properties and interactions.  ...  The generalised Schrödinger equation, eq. (39), is similarly transformed into This connection between model equations and universal formalism of unreduced dynamic complexity reveals also the origin of  ... 
arXiv:1204.3460v3 fatcat:ej7hvm5bpfb4dhd3evau566lka

Propagation Methods for Quantum Molecular Dynamics

R Kosloff
1994 Annual review of physical chemistry (Print)  
The decomposition into a recursive application of the elementary step is performed by a polynomial expansion of the propagator.  ...  A solution for the quantum molecular dynamics can be obtained by recursively applying the elementary mapping step.  ...  By using the results of Equation 4.1, rewriting Equation 4.7, and replacing z with O, = 2n, and where the expansion coefficients a,, are calculated by Equations 4.8 and 4.9.  ... 
doi:10.1146/annurev.pc.45.100194.001045 fatcat:aw4m5a3zc5hjxdgvummgy7o5da

Propagation Methods for Quantum Molecular Dynamics

R Kosloff
1994 Annual review of physical chemistry (Print)  
The decomposition into a recursive application of the elementary step is performed by a polynomial expansion of the propagator.  ...  A solution for the quantum molecular dynamics can be obtained by recursively applying the elementary mapping step.  ...  By using the results of Equation 4.1, rewriting Equation 4.7, and replacing z with O, = 2n, and where the expansion coefficients a,, are calculated by Equations 4.8 and 4.9.  ... 
doi:10.1146/annurev.physchem.45.1.145 fatcat:itb7otvv4vhbjpmzd2a5746qny

Dynamics of solitons in nearly integrable systems

Yuri S. Kivshar, Boris A. Malomed
1989 Reviews of Modern Physics  
Interaction of a Korteweg-de Vries soliton with a moving dipole or a pump wave B. Nonlinear Schrodinger equation C. Sine-Gordon equation 1.  ...  The Inverse Scattering Transform and Perturbation Theory A. General remarks B, Kortewegde Vries equation C. Nonlinear Schrodinger equation D. Sine-Gordon equation E.  ...  ,y)+F(x+y)= f K(x,z)F(z+y)dz=O, in which @'"(x,k ) and of the Jost coefficient a (k) is that they can be analytically continued into the upper half-plane of the complex parameter k.  ... 
doi:10.1103/revmodphys.61.763 fatcat:ztg2x2n7bngxvcl36hbfozbfya

Instabilities, breathers and rogue waves in optics

John M. Dudley, Frédéric Dias, Miro Erkintalo, Goëry Genty
2014 Nature Photonics  
This paper provides an overview of this field, concentrating primarily on propagation in optical fibre systems that exhibit nonlinear breather and soliton dynamics, but also discussing other optical systems  ...  The terminology was first used in the context of an analogy between pulse propagation in optical fibre and wave group propagation on deep water, but has since been generalized to describe many other processes  ...  The analogous physics of nonlinear wave propagation in optics and hydrodynamics has been known for decades, and the focusing nonlinear Schrödinger equation (NLSE) applies to both systems in certain limits  ... 
doi:10.1038/nphoton.2014.220 fatcat:tkw2c5afpzgx7es27rewo7ba3u

Roadmap on optical rogue waves and extreme events

Nail Akhmediev, Bertrand Kibler, Fabio Baronio, Milivoj Belić, Wei-Ping Zhong, Yiqi Zhang, Wonkeun Chang, Jose M Soto-Crespo, Peter Vouzas, Philippe Grelu, Caroline Lecaplain, K Hammani (+26 others)
2016 Journal of Optics  
After all, rogue waves may appear for a multiplicity of reasons and not necessarily only in optical fibers and not only in the process of supercontinuum generation.  ...  We know by now that rogue waves may be generated by lasers, appear in wide aperture cavities, in plasmas and in a variety of other optical systems.  ...  The work of JMSC was supported by MINECO under contract TEC2012-37958-C02-02, by C A M under contract S2013 / MIT-2790, and by the Volkswagen Foundation.  ... 
doi:10.1088/2040-8978/18/6/063001 fatcat:fz3zxhx5yve5zck2pbhy6zye3i

Discrete rogue waves in an array of waveguides

S. Efe, C. Yuce
2015 Physics Letters A  
We predict long-living discrete rogue wave solution of the discrete nonlinear Schrodinger equation.  ...  We study discrete rogue waves in an array of nonlinear waveguides.  ...  In 1983, Peregrine found an analytic solution of the nonlinear Schrodinger equation [1] .  ... 
doi:10.1016/j.physleta.2015.02.031 fatcat:huggp22rfjah3daccnu7zvcf44

Collective Fluctuations in the Dynamics of Adaptation and Other Traveling Waves

O. Hallatschek, L. Geyrhofer
2016 Genetics  
These terms, which are in general not small, control the decay of genetic diversity and, for wave-tip dominated ("pulled") waves, lead to anticorrelations between the tip of the wave and the lagging bulk  ...  and evolution likewise fall into this class of constrained branching random walks.  ...  An equation of the type of Equation B30 is formally equivalent to a Schrödinger equation, which describes the dynamics (in imaginary time) of a quantum particle in a "potential" U ðnÞ ðxÞ: This analogy  ... 
doi:10.1534/genetics.115.181271 pmid:26819246 pmcid:PMC4788118 fatcat:3sp7qhdn7nflbih4pbrserkvia
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