Excited solitons, breathers and periodic waves for a short pulse equation with time-dependent coefficients in relaxing media

Abstract

In this study, the attention is focused on the excitation of Vakhnenko–Parkes (VP) equation with time-dependent coefficients, which can describe the short pulse wave propagation in relaxing media with variable perturbations. Hirota bilinear method is employed to construct three types of analytical solutions, namely, soliton, breather and periodic wave solutions. By utilizing the two free functions involved in the solutions, abundant excited patterns are revealed for the equation. Several examples are taken to demonstrate the novel effects of excited solitons, breathers and periodic waves.