Dark- and bright-rogue-wave solutions for media with long-wave–short-wave resonance

A vector modified Yajima–Oikawa long-wave–short-wave equation is proposed using the zero-curvature presentation. On the basis of the Riccati equations associated with the Lax pair, a method is developed to construct multi-fold classical and generalized Darboux transformations for the vector modified Yajima–Oikawa long-wave–short-wave equation. As applications of the multi-fold classical Darboux transformations and generalized Darboux transformations, various exact solutions for the vector modified long-wave–short-wave equation are obtained, including soliton, breather, and rogue wave solutions.

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The twin properties of rogue waves and homoclinic solutions for some nonlinear wave equations

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2018-0365 ◽

2021 ◽

Vol 0 (0) ◽

Author(s):

Wei Tan ◽

Zhao-Yang Yin

Keyword(s):

Differential Equations ◽

Wave Equations ◽

Rogue Wave ◽

Nonlinear Partial Differential Equations ◽

Rogue Waves ◽

Homoclinic Solutions ◽

Nonlinear Wave Equations ◽

Bilinear Method ◽

Wave Solutions ◽

Rogue Wave Solutions

Abstract The parameter limit method on the basis of Hirota’s bilinear method is proposed to construct the rogue wave solutions for nonlinear partial differential equations (NLPDEs). Some real and complex differential equations are used as concrete examples to illustrate the effectiveness and correctness of the described method. The rogue waves and homoclinic solutions of different structures are obtained and simulated by three-dimensional graphics, respectively. More importantly, we find that rogue wave solutions and homoclinic solutions appear in pairs. That is to say, for some NLPDEs, if there is a homoclinic solution, then there must be a rogue wave solution. The twin phenomenon of rogue wave solutions and homoclinic solutions of a class of NLPDEs is discussed.

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Multi-rogue wave solutions for a generalized integrable discrete nonlinear Schrödinger equation with higher-order excitations

Nonlinear Dynamics ◽

10.1007/s11071-021-06578-x ◽

2021 ◽

Author(s):

Jun Yang ◽

Yan-Li Zhang ◽

Li-Yuan Ma

Keyword(s):

Schrödinger Equation ◽

Nonlinear Schrödinger Equation ◽

Schrodinger Equation ◽

Rogue Wave ◽

Higher Order ◽

Nonlinear Schrodinger Equation ◽

Discrete Nonlinear Schrödinger Equation ◽

Nonlinear Schrödinger ◽

Wave Solutions ◽

Rogue Wave Solutions

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Modeling internal rogue waves in a long wave-short wave resonance framework

Physical Review Fluids ◽

10.1103/physrevfluids.3.124801 ◽

2018 ◽

Vol 3 (12) ◽

Cited By ~ 3

Author(s):

H. N. Chan ◽

R. H. J. Grimshaw ◽

K. W. Chow

Keyword(s):

Rogue Waves ◽

Short Wave ◽

Long Wave ◽

Wave Resonance

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Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2020-0094 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Huanhuan Lu ◽

Yufeng Zhang

Keyword(s):

Vries Equation ◽

Rogue Wave ◽

Rogue Waves ◽

Third Order ◽

First Order ◽

Wave Solutions ◽

De Vries ◽

Rogue Wave Solutions ◽

Bilinear Formulation ◽

Hirota Bilinear

AbstractIn this paper, we analyse two types of rogue wave solutions generated from two improved ansatzs, to the (2 + 1)-dimensional generalized Korteweg–de Vries equation. With symbolic computation, the first-order rogue waves, second-order rogue waves, third-order rogue waves are generated directly from the first ansatz. Based on the Hirota bilinear formulation, another type of one-rogue waves and two-rogue waves can be obtained from the second ansatz. In addition, the dynamic behaviours of obtained rogue wave solutions are illustrated graphically.

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