Chaotic Behaviour of Soliton-Like Pulses in a Driven Modified Kuramoto-Sivashinsky Equation

Abstract

We studied the chaotic behaviour of soliton-like pulses in a modified Kuramoto-Sivashinsky equation under the influence of an external force η( t ): φ t +φ p φ x +αφ x x +βφ x x x +γφ x x x x +νφ=η( t ). Our findings are as follows: (i) when the equation has the Galilean invariance ( p =1), the external force η( t ) does not promote chaotic behaviour of soliton-like pulses and (ii) when the equation does not have the Galilean invariance ( p =2), irregular creations and annihilations of solitons and holes in the traveling state appear which may be due to the interaction of solitons, holes and radiations.