Journal ArticleDOI
Characteristics of solitary wave, homoclinic breather wave and rogue wave solutions in a (2+1)-dimensional generalized breaking soliton equation
TLDR
Using Bell’s polynomials and the extended homoclinic test theory, a bilinear form of the gBS equation is derived, which is explicitly constructed as a soliton solutions for the (2+1)-dimensional generalized breaking soliton equation.Abstract:
We consider a (2+1)-dimensional generalized breaking soliton (gBS) equation, which describes the interaction of the Riemann wave propagated along the y -axis with a long wave propagated along the x -axis. By using Bell’s polynomials, we derive a bilinear form of the gBS equation. Based on the resulting Hirota’s bilinear equation, we explicitly construct its soliton solutions. Furthermore, by using the extended homoclinic test theory, its homoclinic breather waves and rogue waves are well derived, respectively. It is hoped that our results can enrich the dynamical behavior of the gBS-type equations.read more
Citations
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Direct Methods in Soliton Theory (非線形現象の取扱いとその物理的課題に関する研究会報告)
TL;DR: In this article, the authors present a direct and systematic way of finding exact solutions and Backlund transformations of a certain class of nonlinear evolution equations, which they solve exactly using a kind of perturbational approach.
Journal ArticleDOI
Nonlinear wave solutions of the Kudryashov–Sinelshchikov dynamical equation in mixtures liquid-gas bubbles under the consideration of heat transfer and viscosity
TL;DR: In this paper, the exact travelling and solitary wave solutions of the Kudryashov-Sinelshchikov (KS) equation were constructed by implementing the modified mathematical method.
Journal ArticleDOI
Lie group analysis, solitons, self-adjointness and conservation laws of the modified Zakharov-Kuznetsov equation in an electron-positron-ion magnetoplasma
TL;DR: In this paper, a modified Zakharov-Kuznetsov (mZK) equation which describes the ion acoustic drift solitary waves in an electron-positron-ion magnetoplasma is presented.
Journal ArticleDOI
Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrödinger equation
Bang-Qing Li,Yu-Lan Ma +1 more
TL;DR: An extended generalized Darboux transformation method is proposed to construct the hybrid rogue wave and breather solutions for a classical nonlinear Schrodinger equation and an exact link is established between the hybrid solutions and the rogue wave solutions via setting the parameter at special value.
Journal ArticleDOI
Interaction and energy transition between the breather and rogue wave for a generalized nonlinear Schrödinger system with two higher-order dispersion operators in optical fibers
TL;DR: A generalized nonlinear Schrodinger system is investigated in this article, which can be used to describe the optical pulse propagation in inhomogeneous optical fibers with the fourth-and third-order dispersions operators.
References
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Book
Darboux transformations and solitons
V. B. Matveev,Mikhail A. Salle +1 more
TL;DR: In this paper, the authors developed a systematic algebraic approach to solve linear and non-linear partial differential equations arising in soliton theory, such as the non-stationary linear Schrodinger equation, Korteweg-de Vries and Kadomtsev-Petviashvili equations, the Davey Stewartson system, Sine-Gordon and nonlinearSchrodinger equations 1+1 and 2+1 Toda lattice equations, and many others.
Journal ArticleDOI
Optical rogue waves
TL;DR: This work reports the observation of rogue waves in an optical system, based on a microstructured optical fibre, near the threshold of soliton-fission supercontinuum generation—a noise-sensitive nonlinear process in which extremely broadband radiation is generated from a narrowband input.
Journal ArticleDOI
Waves that appear from nowhere and disappear without a trace
TL;DR: In this article, a hierarchy of rational solutions of the nonlinear Schrodinger equation (NLSE) with increasing order and with progressively increasing amplitude is presented. And the authors apply the WANDT title to two objects: rogue waves in the ocean and rational solution of the NLSE.
Journal ArticleDOI
Rogue waves and their generating mechanisms in different physical contexts
TL;DR: In this paper, the authors introduce the concept of rogue waves, which is the name given by oceanographers to isolated large amplitude waves, that occur more frequently than expected for normal, Gaussian distributed, statistical events.
Journal ArticleDOI
Rogue waves and rational solutions of the nonlinear Schrödinger equation
TL;DR: This work can elucidate the appearance of rogue waves in the deep ocean and can be applied to the observation of rogue light pulse waves in optical fibers.
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