Deformed soliton, breather and rogue wave solutions of an inhomogeneous nonlinear Hirota equation

In this paper, an inhomogeneous nonlinear Hirota equation with linear inhomogeneous coefficient and higher-order dispersion is investigated in detail. In describing wave propagation in the ocean and optical fibers, it can be viewed as an approximation which is more accurate than the nonlinear Schro¨dinger equation. Firstly, we modified the Darboux transformation technique to show how to construct solutions of this inhomogeneous equation which owns a non-isospectral Lax pair. Furthermore, the deformed soliton, breather and rogue wave solutions of this equation are studied via the Darboux transformation method, respectively. Finally, properties of those solutions in the inhomogeneous media are discussed to illustrate the influences of variable coefficients.