CK transformations, symmetries, exact solutions and conservation laws of the generalized variable-coefficient KdV types of equations

被引：17
|
作者：
Liu, Hanze [1 ]
Sang, Bo [1 ]
Xin, Xiangpeng [1 ]
Liu, Xiqiang [1 ]
机构：
[1] Liaocheng Univ, Sch Math Sci, Liaocheng 252059, Shandong, Peoples R China
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2019年 / 345卷
基金：
中国国家自然科学基金;
关键词：
CK transformation; Lie group classification; Exact solution; Conservation law; Variable-coefficient equation; INTEGRABLE PROPERTIES; REDUCTIONS; SYSTEMS;
D O I：
10.1016/j.cam.2018.06.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, the improved CK reduction transformation is performed on the generalized variable-coefficient KdV (vc-KdV) type of equation, then these variable-coefficient equations are transformed into its constant-coefficient counterparts under some conditions. Moreover, the complete Lie group classification is presented, all of the point symmetries of the equations are obtained. Furthermore, the exact solutions and conservation laws of the equations are investigated. (C) 2018 Elsevier B.V. All rights reserved.
引用
收藏
页码：127 / 134
页数：8
相关论文
共 50 条
  • [41] Darboux transformation and exact solutions of the variable-coefficient nonlocal Gerdjikov–Ivanov equation
    Yuru Hu
    Feng Zhang
    Xiangpeng Xin
    Hanze Liu
    Theoretical and Mathematical Physics, 2022, 211 : 460 - 472
  • [42] Lax pair, auto-Backlund transformation and conservation law for a generalized variable-coefficient KdV equation with external-force term
    Zhang Yuping
    Liu Jing
    Wei Guangmei
    APPLIED MATHEMATICS LETTERS, 2015, 45 : 58 - 63
  • [43] Conservation laws and exact solutions of the Whitham-type equations
    Shirvani-Sh, Vahid
    Nadjafikhah, Mehdi
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2014, 19 (07) : 2212 - 2219
  • [44] One class of MHD equations: Conservation laws and exact solutions
    Kaptsov, E. I.
    Meleshko, S. V.
    STUDIES IN APPLIED MATHEMATICS, 2023, 151 (03) : 957 - 974
  • [45] Nonlocal conservation laws, nonlocal symmetries and exact solutions of an integrable soliton equation
    Sil, Subhankar
    Sekhar, T. Raja
    Dia Zeidan
    CHAOS SOLITONS & FRACTALS, 2020, 139
  • [46] Infinite Conservation Laws, Continuous Symmetries and Invariant Solutions of Some Discrete Integrable Equations
    Zhang, Yu-Feng
    Zhang, Xiang-Zhi
    Dong, Huan-He
    COMMUNICATIONS IN THEORETICAL PHYSICS, 2017, 68 (06) : 755 - 760
  • [47] Painlevé Test, Generalized Symmetries, Bäcklund Transformations and Exact Solutions to the Third-Order Burgers’ Equations
    Hanze Liu
    Journal of Statistical Physics, 2015, 158 : 433 - 446
  • [48] New Similarity Solutions of a Generalized Variable-Coefficient Gardner Equation with Forcing Term
    Zhou, Jianping
    Wang, Yuan
    Wang, Yang
    Yan, Zhilian
    Wang, Zhen
    SYMMETRY-BASEL, 2018, 10 (04):
  • [49] Breather wave solutions on the Weierstrass elliptic periodic background for the (2<bold>+</bold>1)-dimensional generalized variable-coefficient KdV equation
    Li, Jiabin
    Yang, Yunqing
    Sun, Wanyi
    CHAOS, 2024, 34 (02)
  • [50] Conservation laws for variable coefficient nonlinear wave equations with power nonlinearities
    Huang Ding-Jiang
    Zhou Shui-Geng
    Yang Qin-Min
    CHINESE PHYSICS B, 2011, 20 (07)
12345