Damped variable-coefficient fifth-order modified Korteweg-de Vries equation in fluid mechanics: Solitons, breathers, multi-pole waves and interactions

In this paper, we investigate a damped variable-coefficient fifth-order modified Korteweg-de Vries equation in fluid mechanics. By virtue of the simplified Hirota method, the N-soliton solutions are derived under certain variable-coefficient constraints, where N is a positive integer. Based on the N-soliton solutions, the Hth-order breather and multi-pole solutions are determined through the complex conjugated transformations and limit approach, respectively, where H is a positive integer. Furthermore, we construct the hybrid solutions composed of the first-order breather and one soliton, first-order breather and two solitons, double-pole wave and one soliton, triple-pole wave and one soliton, and first-order breather and double-pole wave. Moreover, we discuss the influences of variable coefficients in the equation on those nonlinear waves graphically.