N-soliton solutions for shallow water waves equations in (1+1) and (2+1) dimensions

被引：26
|
作者：
Wazwaz, Abdul-Majid [1 ]
机构：
[1] St Xavier Univ, Dept Math, Chicago, IL 60655 USA
来源：
APPLIED MATHEMATICS AND COMPUTATION | 2011年 / 217卷 / 21期
关键词：
Shallow water waves equations; Hereman's method; Multiple-soliton solutions; HIROTA 3-SOLITON CONDITION; DE-VRIES EQUATION; TANH-COTH; MODEL-EQUATIONS; SEARCH;
D O I：
10.1016/j.amc.2011.03.048
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A variety of shallow water waves equations in (1 + 1) and (2 + 1) dimensions are investigated. We first show that these models are completely integrable. We next determine multiple-soliton solutions for each equation. The simplified Hirota's bilinear method developed by Hereman will be employed to achieve this goal. A comparison between dispersion relations and the phase shifts will be conducted. (But possess the same coefficients for the polynomials of exponentials.) (C) 2011 Elsevier Inc. All rights reserved.
引用
收藏
页码：8840 / 8845
页数：6
相关论文
共 50 条
  • [1] N-soliton solutions and the Hirota conditions in (1+1)-dimensions
    Ma, Wen-Xiu
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2022, 23 (01) : 123 - 133
  • [2] N-soliton solutions and the Hirota conditions in (2+1)-dimensions
    Ma, Wen-Xiu
    OPTICAL AND QUANTUM ELECTRONICS, 2020, 52 (12)
  • [3] N-soliton solutions and the Hirota conditions in (2+1)-dimensions
    Wen-Xiu Ma
    Optical and Quantum Electronics, 2020, 52
  • [4] AN ALTERNATIVE EXPLICIT CONSTRUCTION OF N-SOLITON SOLUTIONS IN 1+1 DIMENSIONS
    CHAU, LL
    SHAW, JC
    YEN, HC
    JOURNAL OF MATHEMATICAL PHYSICS, 1991, 32 (07) : 1737 - 1743
  • [5] Wronskian N-soliton solutions to a generalized KdV equation in (2+1)-dimensions
    Cheng, Li
    Zhang, Yi
    Ma, Wen-Xiu
    NONLINEAR DYNAMICS, 2023, 111 (02) : 1701 - 1714
  • [6] N-SOLITON SOLUTIONS OF MODEL EQUATIONS FOR SHALLOW-WATER WAVES
    HIROTA, R
    SATSUMA, J
    JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 1976, 40 (02) : 611 - 612
  • [7] Darboux Transformations and N-soliton Solutions of Two (2+1)-Dimensional Nonlinear Equations
    王鑫
    陈勇
    CommunicationsinTheoreticalPhysics, 2014, 61 (04) : 423 - 430
  • [8] Darboux Transformations and N-soliton Solutions of Two (2+1)-Dimensional Nonlinear Equations
    Wang Xin
    Chen Yong
    COMMUNICATIONS IN THEORETICAL PHYSICS, 2014, 61 (04) : 423 - 430
  • [9] N-soliton solutions to a (2+1)-dimensional integrable equation
    Yu, SJ
    Toda, K
    Fukuyama, T
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1998, 31 (50): : 10181 - 10186
  • [10] Backlund transformation and N-soliton solutions for a (2+1)-dimensional nonlinear evolution equation in nonlinear water waves
    Sun, Ya
    Tian, Bo
    Sun, Wen-Rong
    Jiang, Yan
    Wang, Yun-Po
    Huang, Zhi-Ruo
    PHYSICA SCRIPTA, 2014, 89 (07)
12345