A type of bounded traveling wave solutions for the Fornberg-Whitham equation

TL;DR

This paper identifies and characterizes kink-like and anti-kink-like traveling wave solutions for the Fornberg-Whitham equation using bifurcation methods, supported by numerical simulations.

Contribution

It introduces a new type of bounded traveling wave solutions for the Fornberg-Whitham equation and provides their implicit expressions and numerical validation.

Findings

Existence of kink-like and anti-kink-like solutions confirmed

Implicit expressions for solutions derived

Numerical simulations support theoretical results

Abstract

In this paper, by using bifurcation method, we successfully find the Fornberg-Whitham equation has a type of traveling wave solutions called kink-like wave solutions and antikinklike 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 is made. The results show that our theoretical analysis agrees with the numerical simulation.