New Breather and Multiple-Wave Soliton Dynamics for Generalized Vakhnenko–Parkes Equation With Variable Coefficients

Abstract

In investigation is the generalized Vakhnenko–Parkes equation with time-dependent coefficients, which is a new nonlinear model connecting to high-frequency wave propagation in relaxing media with variable perturbations. An extended Hirota bilinear method is proposed to construct soliton, breather, and multiple-wave soliton solutions for the equation. Our research shows that the soliton solutions can degenerate into existing single soliton solutions while the breather and multiple-wave soliton solutions are first obtained. By utilizing the two free functions involved in the solutions, the dynamics of some novel excited breathers and multiple-wave solitons are demonstrated. Our results confirm that the generalized Vakhnenko–Parkes equation possesses rich solution structures and interesting dynamical features, which may be depict various nonlinear wave behaviors of high-frequency waves.