New exact travelling wave solutions for the K(2,2) equation with osmosis dispersion

TL;DR

This paper introduces two new types of travelling wave solutions for the K(2,2) equation with osmosis dispersion, using bifurcation methods, and confirms their properties through numerical simulations.

Contribution

The paper presents the first explicit kink-like and antikink-like travelling wave solutions for the K(2,2) equation with osmosis dispersion, derived via bifurcation analysis.

Findings

Existence of kink-like and antikink-like solutions

Implicit expressions for the solutions

Numerical simulations confirming theoretical results

Abstract

In this paper, by using bifurcation method, we successfully find the K(2,2)equation with osmosis dispersion possess two new types of travelling wave solu tions called kink-like wave solutions and antikink-like wave solutions. They are defined on some semifinal bounded domains and possess properties of kink waves and anti-kink waves. Their implicit expressions are obtained. For some concrete data, the graphs of the implicit functions are displayed, and the numerical simulation of travelling wave system is made by Maple. The results show that our theoretical analysis agrees with the numerical simulation.