LAUSR

In this paper, a generalized inhomogeneous Hirota equation with spatial inhomogeneity and nonlocal nonlinearity is investigated in detail. Firstly, the Darboux transformation is constructed based on corresponding nonisospectral linear eigenvalue problem. This transformation has an essential difference from the isospectral case. Furthermore, the nonautonomous soliton solutions are obtained via the Darboux transformation. Finally, properties of these solutions in the inhomogeneous media are discussed graphically to illustrate the influences of the variable coefficients. It is found that the velocity and amplitude of the solitons can be controlled by the inhomogeneous parameters. Especially, a special two-soliton solution which are localized both in space and time exhibits the feature of the so-called rogue waves but with a zero background.