Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrödinger equation

Feng, Lian-Li; Zhang, Tiantian

doi:10.1016/j.aml.2017.11.011

Cited by 121 publications

(33 citation statements)

References 50 publications

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“…Recently, Ma et al proposed the positive quadratic function to obtain the lump solutions, and some special examples of lump solutions have been found, such as the KdV equation [18,19], the KP equation [20,21], the BKP equation [22], the SK equation [23], the JM equation [24], the shallow water wave equation [25], the coupled Boussinesq equations [26], and nonlinear evolution equation [27,28]. More recently, high-order rogue waves in a variety of soliton equations have been studied, including the generalized Kadomtsev-Petviashvili equation [29], nonlinear Schrödinger equation [30][31][32][33], the Boussinesq equation [34], the breaking soliton equation [35], the Sasa-Satsuma equation [36], the Davey-Stewartson equations [37], the complex short pulse equation [38], and many other equations. More importantly, collision will happen among different solitons.…”

Section: Introductionmentioning

confidence: 99%

High-Order Breather Solutions, Lump Solutions, and Hybrid Solutions of a Reduced Generalized (3 + 1)-Dimensional Shallow Water Wave Equation

Wang

2020

Complexity

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We investigate a reduced generalized (3 + 1)-dimensional shallow water wave equation, which can be used to describe the nonlinear dynamic behavior in physics. By employing Bell's polynomials, the bilinear form of the equation is derived in a very natural way. Based on Hirota's bilinear method, the expression of N-soliton wave solutions is derived. By using the resulting N-soliton expression and reasonable constraining parameters, we concisely construct the high-order breather solutions, which have periodicity in (x, y)-plane. By taking a long-wave limit of the breather solutions, we have obtained the high-order lump solutions and derived the moving path of lumps. Moreover, we provide the hybrid solutions which mean different types of combinations in lump(s) and line wave. In order to better understand these solutions, the dynamic phenomena of the above breather solutions, lump solutions, and hybrid solutions are demonstrated by some figures.

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Section: Introductionmentioning

confidence: 99%

High-Order Breather Solutions, Lump Solutions, and Hybrid Solutions of a Reduced Generalized (3 + 1)-Dimensional Shallow Water Wave Equation

Wang

2020

Complexity

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“…Among these methods, the Hirota direct method is so prompt and effective. Based on this approach, researchers have obtained many di erent kinds of solutions, including lump solutions [13][14][15], breather solutions [16][17][18], rogue wave solutions [19][20][21], interaction solutions, and so on [22][23][24][25][26]. With the help of the Riemann-Hilbert method, people also acquire soliton solutions of integrable hierarchies and coupled systems [27][28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Lump Solutions and Interaction Solutions for the Dimensionally Reduced Nonlinear Evolution Equation

2019

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In this paper, by means of the Hirota bilinear method, a dimensionally reduced nonlinear evolution equation is investigated. Through its bilinear form, lump solutions are obtained. We construct interaction solutions between lump solutions and one soliton solution by choosing quadratic functions and exponential function. Interaction solutions with the combinations of exponential functions and sine function are also given. Meanwhile, the figures of these solutions are plotted. The dynamical characteristics and properties of obtained solutions are discussed, respectively. The results show that the corresponding physical quantities and properties of nonlinear waves are associated with the values of the parameters.

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“…Many scholars planned through NEEs to construct traveling wave solution by implement several methods. The procedures that are well established in recent literature such as extended Kudryashov method [1], Modefied simple equation method [2], New extended (G'/G) expansion method [3][4], Darboux transformation [5], trial solution method [6], Exp-Function Method [7], Multiple Simplest Equation Method [8]. In this paper we implement simple equation method to execute innovative traveling wave solution.…”

Section: Introductionmentioning

confidence: 99%

Breather Wave and Kinky Periodic Wave Solutions of One-Dimensional Oskolkov Equation

Roshid¹,

Bashar²

2019

MMEP

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In this work, we confer the propagation of nonlinear Kinky periodic wave and breather wave for the dominant nonlinear pseudo-parabolic physical models: the one-dimensional Oskolkov equation is explored. By executing simple equation method, compilation of disguise adaptation of exact nonlinear wave solutions with some noteworthy parameters for the Oskolkov equations is accessible. The elements of acquired nonlinear wave arrangements are broke down and delineated in figures by choosing suitable parameters. The simple equation scheme is solid treatment for seeking fundamental nonlinear waves that improve assortment of dynamic models emerges in designing fields. The presentation of this technique is dependable, direct, and easy to execute contrasted with other existing strategies.

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Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrödinger equation

Cited by 121 publications

References 50 publications

High-Order Breather Solutions, Lump Solutions, and Hybrid Solutions of a Reduced Generalized (3 + 1)-Dimensional Shallow Water Wave Equation

High-Order Breather Solutions, Lump Solutions, and Hybrid Solutions of a Reduced Generalized (3 + 1)-Dimensional Shallow Water Wave Equation

Lump Solutions and Interaction Solutions for the Dimensionally Reduced Nonlinear Evolution Equation

Breather Wave and Kinky Periodic Wave Solutions of One-Dimensional Oskolkov Equation

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