Interaction solutions between lump and other solitons of two classes of nonlinear evolution equations

Tang, Yaning; Tao, Siqiao; Zhou, Meiling; Guan, Qing

doi:10.1007/s11071-017-3462-9

Cited by 55 publications

(10 citation statements)

References 25 publications

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“…Then, substituting 5 0 a = into formula (25). From formula (23), we know that the initial velocities in x direction and y direction of lump are lump and the solitary wave will exchange the energy, which will result in that the lump and the solitary wave will not be moving in the original trajectories or moving at the same speeds [46].…”

Section: Lump-soliton Solutionsmentioning

confidence: 99%

Abundant Lump Solutions and Interaction Phenomena to the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation

Lü¹,

Bilige²,

Gao³

et al. 2018

JAMP

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In this paper, we obtained a kind of lump solutions of the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation with the assistance of Mathematica. Some contour plots with different determinant values are sequentially made to show that the corresponding lump solutions tend to zero when 2 2 x y + → ∞. Particularly, lump solutions with specific values of the include parameters are plotted, as illustrative examples. Finally, a combination of stripe soliton and lump soliton is discussed to the KP-BBM equation, in which such a solution presents two different interesting phenomena: lump-kink and lump-soliton. Simultaneously, breather rational soliton solutions are displayed.

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Section: Lump-soliton Solutionsmentioning

confidence: 99%

Abundant Lump Solutions and Interaction Phenomena to the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation

Lü¹,

Bilige²,

Gao³

et al. 2018

JAMP

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“…On the kink wave background, the lump-type wave can move from one asymptotic state to another asymptotic state (Figure 3). In [36,37], the interaction between a kink solitary wave solution and a lump-type wave solution was investigated. However, the obtained results showed that when the lump-type wave solution collided with the kink solitary wave, the lump-type wave solution was completely absorbed or emitted by the kink solitary wave.…”

Section: Theoremmentioning

confidence: 99%

Lump-Type Wave and Interaction Solutions of the Bogoyavlenskii–Kadomtsev–Petviashvili Equation

Wang

Fang

2020

Complexity

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Lump-type wave solution of the Bogoyavlenskii–Kadomtsev–Petviashvili equation is constructed by using the bilinear structure and Hermitian quadratic form. The dynamical behaviors of lump-type wave solution are investigated and presented analytically and graphically. Furthermore, we discuss the interaction between a lump-type wave and a kink wave solution. Absorb-emit interaction between two kinds of solitary wave solutions is shown. This kind of interaction solution can be regarded as a lump-type wave which propagates on the kink wave background.

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“…e solutions have been graphically plotted using the Wolfram Mathematica software while a detailed physical evolution of results is made. Tang et al [42] reported interaction based soliton results for BLMP and evolutionary equations via a direct approach. It is further stated that a lump seemed from the one side of the soliton wave and dispersed gradually from this side of the soliton wave, after approaching the extreme departure at time zero, the lump gradually treads upon the further side of the soliton wave and last swallowed by the other side.…”

Section: Introductionmentioning

confidence: 99%

Travelling Wave Solutions of Nonlinear Evolution Problem Arising in Mathematical Physics through (G′/G)-Expansion Scheme

Fan

Sun

Liu

et al. 2022

Mathematical Problems in Engineering

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This article deals with the application of well-known (G′/G)-expansion to investigate the travelling wave solutions of nonlinear evolution problems including the Boussinesq equation, Klein–Gordon equation, and sine-Gordon equation as these problems appear frequently in mathematical physics. The beauty of the suggested method is to transform the highly nonlinear evolution equation into a system of nonlinear algebraic equations by means of trial solution and auxiliary equation. It is found that the presented approach is simple, efficient, has a less computational cost, and produced rational trigonometric solutions. In order to investigate the novel results, various simulations have been executed. It is renowned that all solutions are in the form of soliton with a single hump and singular which is travelling as time increases gradually. It travels as time travel with the same shape. Moreover, as A2 decreases the amplitude of the solutions decreases. A comparative study illustrates that some of the obtained solution matches with the existing results against particular values of parameters and various new travelling wave solution attained the first time. The method seems more appropriate by means of a computational work. It can also be extended to demonstrate the behavior of other physical models of physical nature.

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Interaction solutions between lump and other solitons of two classes of nonlinear evolution equations

Cited by 55 publications

References 25 publications

Abundant Lump Solutions and Interaction Phenomena to the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation

Abundant Lump Solutions and Interaction Phenomena to the Kadomtsev-Petviashvili-Benjamin-Bona-Mahony Equation

Lump-Type Wave and Interaction Solutions of the Bogoyavlenskii–Kadomtsev–Petviashvili Equation

Travelling Wave Solutions of Nonlinear Evolution Problem Arising in Mathematical Physics through (G′/G)-Expansion Scheme

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