Remarks on chaotic and fractal patterns based on variable separation solutions of (2+1)-dimensional general KdV equation

被引：3
作者：
Dai, Chao-Qing [1 ]
Wang, Yue-Yue [1 ]
机构：
[1] Zhejiang Agr & Forestry Univ, Sch Sci, Linan 311300, Zhejiang, Peoples R China
来源：
APPLIED MATHEMATICS LETTERS | 2016年 / 56卷
关键词：
General Korteweg-de Vries equation; Same results from different; tanh-function methods; Chaotic and fractal patterns; Divergent structure; DE-VRIES SYSTEM; NONLINEAR SCHRODINGER-EQUATION; DROMION-LIKE STRUCTURES; COEFFICIENT; EXCITATIONS; MODELS;
D O I：
10.1016/j.aml.2015.11.014
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We obtain eleven types of variable separation solutions for the (2 + 1)-dimensional general KdV equation by means of the extended tanh-function method, modified tanh-function method and improved tanh-function method with radical sign combine form ansatz. However, solutions obtained by different methods are essentially same. Moreover, when we construct chaotic and fractal patterns for a special component based on variable separation solution, we must consider solution expression of the other component in order to avoid many divergent and un-physical structures. (C) 2015 Elsevier Ltd. All rights reserved.
引用
收藏
页码：10 / 16
页数：7
相关论文
共 22 条
  • [1] ABLOWTIZ MJ, 1991, SOLITON NONLINEAR EV
  • [2] EXACTLY SOLVABLE SUPERSYMMETRIC QUANTUM-MECHANICS
    ARAI, A
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1991, 158 (01) : 63 - 79
  • [3] METHOD TO GENERATE SOLVABLE NONLINEAR EVOLUTION EQUATIONS
    CALOGERO, F
    [J]. LETTERE AL NUOVO CIMENTO, 1975, 14 (12): : 443 - 447
  • [4] SYMMETRY REDUCTIONS AND EXACT-SOLUTIONS OF SHALLOW-WATER WAVE-EQUATIONS
    CLARKSON, PA
    MANSFIELD, EL
    [J]. ACTA APPLICANDAE MATHEMATICAE, 1995, 39 (1-3) : 245 - 276
  • [5] The novel solitary wave structures and interactions in the (2+1)-dimensional Kortweg-de Vries system
    Dai, Chao-Qing
    Wang, Yue-Yue
    [J]. APPLIED MATHEMATICS AND COMPUTATION, 2009, 208 (02) : 453 - 461
  • [6] Novel variable separation solutions and exotic localized excitations via the ETM in nonlinear soliton systems
    Dai, CQ
    Zhang, JF
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2006, 47 (04)
  • [7] Korteweg D J., 1895, PHILOS MAG, V5, P422, DOI [10.1080/14786449508620739, DOI 10.1080/14786449508620739]
  • [8] Interactions of dromion-like structures in the (1+1) dimension variable coefficient nonlinear Schrodinger equation
    Liu, Wen-Jun
    Huang, Long-Gang
    Li, Yan-Qing
    Pan, Nan
    Lei, Ming
    [J]. APPLIED MATHEMATICS LETTERS, 2015, 39 : 91 - 95
  • [9] Dromion-like structures in the variable coefficient nonlinear Schrodinger equation
    Liu, Wen-Jun
    Tian, Bo
    Lei, Ming
    [J]. APPLIED MATHEMATICS LETTERS, 2014, 30 : 28 - 32
  • [10] Be careful with the equivalence of different ansatz of improved tanh-function method for nonlinear models
    Lou, Mu-Ren
    Zhang, Yu-Peng
    Kong, Liang-Qian
    Dai, Chao-Qing
    [J]. APPLIED MATHEMATICS LETTERS, 2015, 48 : 23 - 29
123