KdV hierarchy with time-dependent coefficients: Lax integrability, bilinear Backlund transformation and soliton solutions

被引：3
|
作者：
Zhang, Sheng [1 ]
Zhu, Ran [1 ]
机构：
[1] Bohai Univ, Sch Math & Phys, Jinzhou 121013, Peoples R China
来源：
OPTIK | 2017年 / 142卷
关键词：
KdV hierarchy with time-dependent coefficients; Lax integrability; Bilinear BT; Soliton solution; HAMILTONIAN-STRUCTURE; EQUATION; COUPLINGS;
D O I：
10.1016/j.ijleo.2017.06.018
中图分类号：
O43 [光学];
学科分类号：
070207 ; 0803 ;
摘要：
Starting from the linear problems, we first derive a new Lax integrable Korteweg-de Vries (KdV) hierarchy with time-dependent coefficients. Then a bilinear Backlund transformation (BT) of the variable-coefficient KdV (vcKdV) equation contained in the KdV hierarchy is given. Based on the given bilinear BT, one-soliton solution, two-soliton solution and three-soliton solution are obtained. From these obtained soliton solutions, a uniform formula of explicit n-soliton solutions of the vcKdV equation is summarized. It is graphically shown that the dynamical evolutions of such soliton solutions with time-dependent functions of the KdV hierarchy possess time-varying speeds in the process of propagations. (C) 2017 Elsevier GmbH. All rights reserved.
引用
收藏
页码：463 / 469
页数：7
相关论文
共 50 条
  • [21] On periodic wave solutions of the KdV6 equation via bilinear Backlund transformation
    Zhao, Zhonglong
    Chen, Yong
    Han, Bo
    OPTIK, 2017, 140 : 10 - 17
  • [22] Topological Soliton Solutions of (2+1)-dimensional KdV Equation with Power Law Nonlinearity and Time-dependent Coefficients
    Triki, Houria
    Milovic, Daniela M.
    Hayat, T.
    Aldossary, Omar M.
    Biswas, Anjan
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2011, 12 (1-8) : 35 - 43
  • [23] Equivalent transformation and integrability of the nonlinear Schrödinger equations with time-dependent coefficients 
    Liu, Hanze
    NUCLEAR PHYSICS B, 2023, 994
  • [24] A New Simplified Bilinear Method for the N-Soliton Solutions for a Generalized FmKdV Equation with Time-Dependent Variable Coefficients
    Alquran, Marwan
    Jaradat, H. M.
    Al-Shara', Safwan
    Awawdeh, Fadi
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2015, 16 (06) : 259 - 269
  • [25] On soliton solutions for the Fitzhugh-Nagumo equation with time-dependent coefficients
    Triki, Houria
    Wazwaz, Abdul-Majid
    APPLIED MATHEMATICAL MODELLING, 2013, 37 (06) : 3821 - 3828
  • [26] MULTIPLE SOLITON SOLUTIONS OF THE MODEL mKdV WITH TIME-DEPENDENT VARIABLE COEFFICIENTS
    Abdalla, Mukhtar Y. Y.
    Younies, Bakery A. E.
    Adam, Haroon D. S.
    Adam, Ahmed M. I.
    Arko, Yagoub A. S.
    Jazmati, Mohammad S.
    THERMAL SCIENCE, 2024, 28 (6B): : 5029 - 5036
  • [27] Soliton solutions of some nonlinear evolution equations with time-dependent coefficients
    HITENDER KUMAR
    ANAND MALIK
    FAKIR CHAND
    Pramana, 2013, 80 : 361 - 367
  • [28] Soliton solutions of some nonlinear evolution equations with time-dependent coefficients
    Kumar, Hitender
    Malik, Anand
    Chand, Fakir
    PRAMANA-JOURNAL OF PHYSICS, 2013, 80 (02): : 361 - 367
  • [29] Soliton solutions and Backlund transformation for the Kupershmidt five-field lattice: A bilinear approach
    Tam, HW
    Hu, XB
    APPLIED MATHEMATICS LETTERS, 2002, 15 (08) : 987 - 993
  • [30] Soliton Solutions and Bilinear Backlund Transformation for Generalized Nonlinear Schrodinger Equation with Radial Symmetry
    Jiang Yan
    Tian Bo
    Liu Wen-Jun
    Sun Kun
    Qu Qi-Xing
    COMMUNICATIONS IN THEORETICAL PHYSICS, 2010, 54 (04) : 635 - 640
12345