Analytical solutions and rogue waves in (3+1)-dimensional nonlinear Schrödinger equation

Ma, Zheng-Yi; Ma, Song-Ya

doi:10.1088/1674-1056/21/3/030507

Cited by 33 publications

(16 citation statements)

References 32 publications

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“…Recently, Akhmediev et al [1] presented explicit forms of the rational solutions to describe them by the deformed Darboux transformation. Yan [18] and Ma et al [10] investigated the nonautonomous rogue waves in one-dimensional and three-dimensional generalized nonlinear Schrödinger equations with variable coefficients by the similarity transformation and direct ansatz. More recently, Dai et al [7] discussed their propagation behaviors in a variable coefficient higher-order nonlinear Schrödinger equation by a similarity transformation connected with the constant coefficient Hirota equation.…”

Section: Introductionmentioning

confidence: 99%

Two kinds of breather solitary wave and rogue wave solutions for the (3+1)-dimensional Kadomtsev-Petviashvili equation

Xu¹,

Chen²,

Dai³

2017

J. Nonlinear Sci. Appl.

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In this paper, the (3+1)-dimensional Kadomtsev-Petviashvili equation is investigated. Two kinds of periodic breather solitary wave and rogue wave solutions are obtained by using the two-wave method and the homoclinic breather limit approach with the aid of Maple. Deflection of rogue wave varying with the seed solution u 0 is investigated. c 2017 all rights reserved.Keywords: (3+1)-dimensional Kadomtsev-Petviashvili equation, homoclinic breather limit approach, two-wave method, rational breather solutions, rogue wave. 2010 MSC: 35G20, 35C05, 35C07.

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Section: Introductionmentioning

confidence: 99%

Two kinds of breather solitary wave and rogue wave solutions for the (3+1)-dimensional Kadomtsev-Petviashvili equation

Xu¹,

Chen²,

Dai³

2017

J. Nonlinear Sci. Appl.

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“…For describing the natural nonlinear phenomenon, the nonlinear Schrödinger equation is a fundamental model which is widely applied in nonlinear science and is also widely used in studying the existence of rogue waves and their structures [16,17,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Rogue wave solutions of the nonlinear Schrödinger equation with variable coefficients

Liu

Mei-ping

et al. 2015

Pramana - J Phys

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In this paper, a unified formula of a series of rogue wave solutions for the standard (1+1)-dimensional nonlinear Schrödinger equation is obtained through exp-function method. Further, by means of an appropriate transformation and previously obtained solutions, rogue wave solutions of the variable coefficient Schrödinger equation are also obtained. Two free functions of time t and several arbitrary parameters are involved to generate a large number of wave structures.

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“…For describing the natural nonlinear phenomenon, the nonlinear Schrödinger equation is a fundamental model which is widely applied in the nonlinear science and is also widely used in studying the existence of rogue waves and their structures (Bludov et al, 2009;Guo and Ling, 2011;Ma and Ma, 2012;Yan, 2010;Wang et al, 2011a, b;Ankiewicz et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Rogue waves in the (2+1)-dimensional nonlinear Schrodinger equations

Liu

Wang

Dai

et al. 2015

International Journal of Numerical Methods for Heat &Amp; Fluid Flow

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Purpose -The purpose of this paper is to construct analytical solutions of the (2+1)-dimensional nonlinear Schrodinger equations, and the existence of rogue waves and their localized structures are studied. Design/methodology/approach -Function transformation and variable separation method are applied to the (2+1)-dimensional nonlinear Schrodinger equations. Findings -A series of analytical solutions including rogue wave solutions for the (2+1)-dimensional nonlinear Schrodinger equations are constructed. Localized structures of rogue waves confirm the presence of large amplitude wave wall. Research limitations/implications -The localized structures of rogue waves are displayed by analytical solutions and figures. The authors just find some of them and others still to be found. Originality/value -These results may help to investigate the localized structures and the behavior of rogue waves for nonlinear evolution equations. Applying two different function transformations and variable separation functions to two different states of the equations, respectively, to construct the solutions of the (2+1)-dimensional nonlinear Schrodinger equations. Rogue wave solutions are enumerated and their figures are partly displayed.

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Analytical solutions and rogue waves in (3+1)-dimensional nonlinear Schrödinger equation

Cited by 33 publications

References 32 publications

Two kinds of breather solitary wave and rogue wave solutions for the (3+1)-dimensional Kadomtsev-Petviashvili equation

Two kinds of breather solitary wave and rogue wave solutions for the (3+1)-dimensional Kadomtsev-Petviashvili equation

Rogue wave solutions of the nonlinear Schrödinger equation with variable coefficients

Rogue waves in the (2+1)-dimensional nonlinear Schrodinger equations

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