Exact Periodic Wave Solutions of a Singular Integrable Equation

Abstract

In this paper, theory of dynamical systems is employed to investigate periodic waves of a singular integrable equation. These periodic waves contain smooth periodic waves, periodic cusp waves and periodic cusp loop waves. Under fixed parameter conditions, their exact parametric expressions are given.

Keywords:

• Singular integrable equation
• closed orbit
• smooth periodic wave
• periodic cusp wave
• periodic cusp loop wave

AMS Subject Classification:

• 35Q51
• 35Q58
• 37K50