Lump solutions and interaction behaviors to the (2+1)-dimensional extended shallow water wave equation

被引：14

作者：

Cheng, Wenguang ^{[1
,2
]}

Xu, Tianzhou ^{[1
]}

机构：

[1] Beijing Inst Technol, Sch Math & Stat, Beijing 100081, Peoples R China

[2] Yuxi Normal Univ, Dept Math, Yuxi 653100, Peoples R China

来源：

MODERN PHYSICS LETTERS B | 2018年 / 32卷 / 31期

关键词：

Lump solutions; interaction solutions; Hirota bilinear form; (2+1)-dimensional extended shallow water wave equation; NONLINEAR EVOLUTION-EQUATIONS; HIROTA BILINEAR EQUATION; PETVIASHVILI I EQUATION; SAWADA-KOTERA EQUATION; KP EQUATION; BACKLUND TRANSFORMATION; SCHRODINGER-EQUATION; SOLITON-SOLUTIONS; KINK SOLUTIONS; BKP EQUATION;

D O I：

10.1142/S0217984918503876

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

In this paper, the exact solutions to the (2 + 1)-dimensional extended shallow water wave (SWW) equation are investigated by using its bilinear form and ansatz techniques. Following the method given by Ma [Phys. Lett. A 379 (2015) 1975-1978], two classes of lump solutions are constructed by searching for positive quadratic function solutions to the associated bilinear equation. Furthermore, two kinds of interaction solutions between a lump and solitary waves are presented by taking the solution of the associated bilinear equation as a linear combination function of a quadratic function and the double exponential function, one of which is the interaction solution between a lump and an exponentially decayed soliton, and the other one is the interaction solution between a lump and an exponentially decayed twin soliton. Finally, some figures are given to illustrate the dynamic properties of these obtained solutions.

引用

页数：10

共 61 条

[1]

Ablowitz M., 1991, Soliton, Nonlinear Evolution Equations and Inverse Scattering

[2] How to excite a rogue wave [J].

Akhmediev, N. ;

Soto-Crespo, J. M. ;

Ankiewicz, A. .

PHYSICAL REVIEW A, 2009, 80 (04)

[3] MODULATION INSTABILITY AND PERIODIC-SOLUTIONS OF THE NONLINEAR SCHRODINGER-EQUATION [J].

AKHMEDIEV, NN ;

KORNEEV, VI .

THEORETICAL AND MATHEMATICAL PHYSICS, 1986, 69 (02) :1089-1093

[4]

Aranson IS, 2017, Advances in dynamics, patterns, cognition: challenges in complexity

[5] Vector Rogue Waves and Baseband Modulation Instability in the Defocusing Regime [J].

Baronio, Fabio ;

Conforti, Matteo ;

Degasperis, Antonio ;

Lombardo, Sara ;

Onorato, Miguel ;

Wabnitz, Stefan .

PHYSICAL REVIEW LETTERS, 2014, 113 (03)

[6] Exact solutions of shallow water wave equations by using the (G′/G)-expansion method [J].

Bekir, Ahmet ;

Aksoy, Esin .

WAVES IN RANDOM AND COMPLEX MEDIA, 2012, 22 (03) :317-331

[7] Nonlocal symmetries of the Hirota-Satsuma coupled Korteweg-de Vries system and their applications: Exact interaction solutions and integrable hierarchy [J].

Chen, Junchao ;

Xin, Xiangpeng ;

Chen, Yong .

JOURNAL OF MATHEMATICAL PHYSICS, 2014, 55 (05)

[8] A Pair of Resonance Stripe Solitons and Lump Solutions to a Reduced (3+1)-Dimensional Nonlinear Evolution Equation [J].

Chen, Mei-Dan ;

Li, Xian ;

Wang, Yao ;

Li, Biao .

COMMUNICATIONS IN THEORETICAL PHYSICS, 2017, 67 (06) :595-600

[9] Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic function solutions to (1+1)-dimensional dispersive long wave equation [J].

Chen, Y ;

Wang, Q .

CHAOS SOLITONS & FRACTALS, 2005, 24 (03) :745-757

[10] Nonlocal symmetry and exact solutions of the (2+1)-dimensional breaking soliton equation [J].

Cheng, Wen-guang ;

Li, Biao ;

Chen, Yong .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2015, 29 (1-3) :198-207

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