Integrability and analytic solutions for a damped variable-coefficient fifth-order modified Korteweg-de Vries equation for the surface waves in a strait or large channel

Abstract

Investigations on the variable-coefficient nonlinear partial differential equations attract people's attention. In this paper, we investigate a damped variable-coefficient fifth-order modified Korteweg-de Vries equation for some fluids and cosmic plasmas. Under certain variable-coefficient constraints, we find that the equation is Painlevé integrable. By virtue of the real and complex simplified Hirota procedures, multiple real and complex soliton solutions are derived. Via the soliton wave ansatz method, we obtain some other analytic solutions such as the kink, bell, singular and periodic soliton solutions. Moreover, we discuss the influences of variable coefficients in the equation on those solitons graphically.