EXISTENCE OF KINK AND UNBOUNDED TRAVELING WAVE SOLUTIONS OF THE CASIMIR EQUATION FOR THE ITO SYSTEM

Temesgen Desta Leta; Jibin Li

doi:10.11948/2017039

2017 Volume 7 Issue 2

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Temesgen Desta Leta, Jibin Li. EXISTENCE OF KINK AND UNBOUNDED TRAVELING WAVE SOLUTIONS OF THE CASIMIR EQUATION FOR THE ITO SYSTEM[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 632-643. doi: 10.11948/2017039

Citation:

Temesgen Desta Leta, Jibin Li. EXISTENCE OF KINK AND UNBOUNDED TRAVELING WAVE SOLUTIONS OF THE CASIMIR EQUATION FOR THE ITO SYSTEM[J]. Journal of Applied Analysis & Computation, 2017, 7(2): 632-643. doi: 10.11948/2017039

EXISTENCE OF KINK AND UNBOUNDED TRAVELING WAVE SOLUTIONS OF THE CASIMIR EQUATION FOR THE ITO SYSTEM

Mathematics Department, Zhejiang Normal University, 688 Yingbin Avenue, 321004 Jinhua, China

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Abstract

Abstract

This paper study the traveling wave solutions of the Casimir equation for the Ito system. Since the derivative function of the wave function is a solution of a planar dynamical system, from which the exact parametric representations of solutions and bifurcations of phase portraits can be obtained. Thus, we show that corresponding to the compacton solutions of the derivative function system, there exist uncountably infinite kink wave solutions of the wave equation. Corresponding to the positive or negative periodic solutions and homoclinic solutions of the derivative function system, there exist unbounded wave solutions of the wave function equation.
- Kink wave solution /
- unbounded wave solution /
- bifurcation /
- exact solution /
- Casimir equation for the Ito system
MSC: 34A05;34C25-28;34M55;35Q51;35Q53;58F05;58F14;58F30;35C05;35C07;34C60

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References

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