Exact soliton solutions for the interaction of few-cycle-pulse with nonlinear medium

Abstract

We study the Panilevé property of the coupled equations describing the interaction of few-cycle-pulse with nonlinear medium. And we use the consistent tanh expansion (CTE) method to search for exact interaction soliton solutions of the coupled equations. Many interaction solutions are obtained, such as the one kink-one periodic wave interaction solution, one kink-two periodic waves interaction solution, one kink-one dipole soliton interaction solution, one kink-two dipole solitons interaction solution, and one kink-soliton-one periodic wave interaction solution. We also obtain the kink–kink interaction by using Painlevé truncated expansion method.