BIFURCATIONS OF TRAVELING WAVE SOLUTIONS IN A MICROSTRUCTURED SOLID MODEL

被引：7
|
作者：
Li, Jibin [1 ,2 ]
Chen, Guanrong [3 ]
机构：
[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China
[2] Kunming Univ Sci & Technol, Ctr Nonlinear Sci Studies, Kunming 650093, Yunnan, Peoples R China
[3] City Univ Hong Kong, Dept Elect Engn, Hong Kong, Hong Kong, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2013年 / 23卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Kink wave solution; periodic wave solution; breaking wave solution; second class of singular traveling wave system; bifurcation; micro-structured solid model;
D O I：
10.1142/S0218127413500090
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The traveling wave system of a microstructured solid model belongs to the second class of singular traveling wave equations studied in [Li et al., 2009]. In this paper, by using methods from dynamical systems theory, bifurcations of phase portraits of such a traveling wave system are analyzed in its corresponding parameter space. The existence of kink wave solutions and uncountably infinitely many bounded solutions is proved. Moreover, the exact parametric representations of periodic solutions and homoclinic orbits are obtained.
引用
收藏
页数：18
相关论文
共 50 条
  • [1] Bifurcations of traveling wave solutions for the magma equation
    Geng, Yixiang
    Zhang, Lixiang
    APPLIED MATHEMATICS AND COMPUTATION, 2010, 217 (04) : 1741 - 1748
  • [2] Bifurcations of traveling wave solutions for an integrable equation
    Li, Jibin
    Qiao, Zhijun
    JOURNAL OF MATHEMATICAL PHYSICS, 2010, 51 (04)
  • [3] The Bifurcations of Traveling Wave Solutions of the Kundu Equation
    Yi, Yating
    Liu, Zhengrong
    JOURNAL OF APPLIED MATHEMATICS, 2013,
  • [4] Bifurcations of Traveling Wave Solutions of a Nonlinear Wave Model Created by Diffraction in Periodic Media
    Li, Jibin
    Chen, Fengjuan
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2016, 26 (02):
  • [5] Study on bifurcations of traveling wave solutions of Boussinesq equation
    Business School, University of Shanghai for Science and Technology, Shanghai 200093, China
    Shanghai Ligong Daxue Xuebao, 2007, 2 (125-128):
  • [6] Bifurcations of traveling wave solutions for a class of the nonlinear equations
    Zhao, Xiaoshan
    Wang, Mingchun
    Xu, Wei
    APPLIED MATHEMATICS AND COMPUTATION, 2008, 197 (01) : 228 - 242
  • [7] BIFURCATIONS OF TRAVELING WAVE SOLUTIONS AND EXACT SOLUTIONS FOR THE GENERALIZED SCHRODINGER EQUATION
    Zhang, Jianming
    Li, Shuming
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2011, 21 (09): : 2623 - 2628
  • [8] Bifurcations and Exact Traveling Wave Solutions in Two Nonlinear Wave Systems
    Zhou, Yan
    Zhuang, Jinsen
    Li, Jibin
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2021, 31 (06):
  • [9] Bifurcations of traveling wave solutions for four classes of nonlinear wave equations
    Li, JB
    Chen, GR
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2005, 15 (12): : 3973 - 3998
  • [10] Bifurcations and Exact Traveling Wave Solutions for a Model of Nonlinear Pulse Propagation in Optical Fibers
    Li, Jibin
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2014, 24 (06):
12345