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Feiting Fan, Yuqian Zhou, Xingwu Chen. TRAVELING WAVES AND THEIR EVOLUTION FOR THE ZK(N, 2N, -N) EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 2959-2980. doi: 10.11948/20210074
Citation: Feiting Fan, Yuqian Zhou, Xingwu Chen. TRAVELING WAVES AND THEIR EVOLUTION FOR THE ZK(N, 2N, -N) EQUATION[J]. Journal of Applied Analysis & Computation, 2021, 11(6): 2959-2980. doi: 10.11948/20210074
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TRAVELING WAVES AND THEIR EVOLUTION FOR THE ZK(N, 2N, -N) EQUATION

  • 1.

    Department of Mathematics, Sichuan University, Chengdu 610064, China

  • 2.

    College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China

  • Corresponding author: Email: xingwu.chen@hotmail.com(X. Chen)
  • Fund Project: The second author was supported by the China Postdoctoral Science Foundation (No. 2016M602663) and the third author was supported by National Natural Science Foundation of China (No. 11871355)
    Abstract

  • In this paper, using the approach of dynamical systems we investigate the traveling waves for the ZK(n, 2n, -n) equation including the types and evolution of traveling waves. The traveling wave problem is converted into the analysis of phase portraits of the corresponding traveling wave system, which is 5-parametric and has a singular line in its phase space. The orbits passing through this singular line in phase portraits are determined by a time rescaling. After converting the orbits in these phase portraits into traveling waves, we state all types of traveling waves and give at least one exact traveling wave solution for each type of bounded traveling waves in our main results. Finally, we discuss the evolution of these traveling waves among themselves when parameters vary by the bifurcations happening in the phase portraits of the traveling wave system.
    MSC: 34C37, 34C23, 58Z05, 74J30
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