Soliton and breather solutions for a fifth-order modified KdV equation with a nonzero background

Abstract

We investigate an integrable fifth-order modified KdV equation, which contains the fifth-order dispersion and relevant higher-order nonlinear terms, on the line with a nonzero constant background via the Riemann–Hilbert method. As an application, the explicit soliton and breather solutions are obtained. Some figures are also presented to depict the soliton and breather behaviors of the fifth-order modified KdV equation.