Resonance and deflection of multi-soliton to the (2+1)-dimensional Kadomtsev–Petviashvili equation

Xu, Zhijie; Chen, Hanlin; Jiang, Murong; Dai, Zhengde; Chen, Wei

doi:10.1007/s11071-014-1452-8

Cited by 24 publications

(10 citation statements)

References 19 publications

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“…On the basis of the bilinear equation (3), we find the periodic wave-type solutions through the three-wave method 31,32 for the extended (3+1)-dimensional JM equation by setting the form…”

Section: Periodic Wave-type Solutions To the Extended (3+1)-dimensionmentioning

confidence: 99%

On integrability of the extended (3+1)‐dimensional Jimbo‐Miwa equation

Liu

Yang

Feng

2019

Math Methods in App Sciences

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By applying the binary bell polynomial scheme, the bilinear form, Bäcklund Transformations, and lax pairs of an extended (3+1)-dimensional Jimbo-miwa (JM) equation are constructed. Next, periodic wave-type solutions can also be obtained to the extended (3+1)-dimensional JM equation through the three-wave method with the help of maple. Finally, a test function of the sech-function method is utilized to get solitary waves of this study problem. These new results can help us better understand interesting physical phenomena and mechanism. KEYWORDS binary bell polynomial scheme, extended (3+1)-dimensional JM equation, bäcklund transformations and Lax pairs, periodic wave-Type solutions, Solitary Waves MSC CLASSIFICATION 35L05; 35C08; 35Q35 This equation was firstly proposed by A. M. Wazwaz to study its one-soliton solution, two-soliton solution, and multi-soliton solutions of Equation (1) by utilizing the simplified Hirota bilinear method. 25 Meanwhile, Sun and Chen obtained the lump solutions of Equation (1). 26 Manafian 27 used the Hirota bilinear method of a new combination of exponential function, trigonometric function, and hyperbolic functions to obtain new periodic solitary wave solutions, etc. 27-29

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“…On the basis of the bilinear equation (3), we find the periodic wave-type solutions through the three-wave method 31,32 for the extended (3+1)-dimensional JM equation by setting the form…”

Section: Periodic Wave-type Solutions To the Extended (3+1)-dimensionmentioning

confidence: 99%

On integrability of the extended (3+1)‐dimensional Jimbo‐Miwa equation

Liu

Yang

Feng

2019

Math Methods in App Sciences

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“…It is obvious that u 0 < -1 6 (cp 2 + 4α) is required so that the conditions Ω 2 > 0, b 2 1 > 0, and 0 < p 2 < -4α+6u 0 c can be satisfied in Eq. (9). Notice that u 0 can be taken as an arbitrary real number because the speed of propagating wave α can be arbitrary (only corresponding to the direction and speed propagating wave on the x-axis).…”

Section: Cross Soliton Of Ytsfmentioning

confidence: 99%

“…It was verified that the existence of two solitons having the structures peculiar to a higher-dimensionality may contribute to the variety of the dynamics of nonlinear waves [1][2][3]. Thereby, seeking for exact solution and studying dynamical behavior [4][5][6][7] of solutions are very significant in physics, mathematics, and nonlinear science fields for understanding the complexity and variety of dynamics determined by high-dimensional nonlinear evolution equation [8][9][10]. In soliton theory, the soliton solutions are obtained by the use of the inverse scattering method, Bäcklund transformation, Darboux transformation, Painlevè method, Hirota method, the tanh method, the generalized Riccati equation expansion method, homoclinic test method, etc.…”

Section: Introductionmentioning

confidence: 99%

Cross soliton and breather soliton for the $(3+1)$-dimensional Yu–Toda–Sasa–Fukuyama equation

Pan

2019

Adv Differ Equ

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Cross-soliton solution, breather soliton, periodic solitary solution, and doubly periodic solution are obtained by using an extended homoclinic test approach with perturbation parameter u 0 and complexity of parameters, respectively. Dynamical feature of cross soliton flow including degeneracy of soliton with different directions, retroflexion of breather soliton for YTSF equation is investigated using the parameter perturbation method. Result shows that the value range of constant equilibrium solution can determine the dynamics of cross soliton for a higher dimensional nonlinear system.

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“…Also, after applying a generalized variable-coefficient algebraic method [3] In this work, a novel approach of seeking rogue wave solution, the homoclinic breather limit approach [5,15], is proposed. By using the homoclinic breather limit approach and two-wave method [6,16,17], we obtain two kinds of breather solitary wave and rogue wave solutions. Furthermore, we also investigate differently mechanical features of these wave solutions [19,20].…”

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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Resonance and deflection of multi-soliton to the (2+1)-dimensional Kadomtsev–Petviashvili equation

Cited by 24 publications

References 19 publications

On integrability of the extended (3+1)‐dimensional Jimbo‐Miwa equation

On integrability of the extended (3+1)‐dimensional Jimbo‐Miwa equation

Cross soliton and breather soliton for the $(3+1)$-dimensional Yu–Toda–Sasa–Fukuyama equation

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

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