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

We use the 1-fold Darboux transformation (DT) of an inhomogeneous nonlinear Schrödinger equation (INLSE) to construct the deformed-soliton, breather, and rogue wave solutions explicitly. Furthermore, the obtained first-order deformed rogue wave solution, which is derived from the deformed breather solution through the Taylor expansion, is different from the known rogue wave solution of the nonlinear Schrödinger equation (NLSE). The effect of inhomogeneity is fully reflected in the variable height of the deformed soliton and the curved background of the deformed breather and rogue wave. By suitably adjusting the physical parameter, we show that a desired shape of the rogue wave can be generated. In particular, the newly constructed rogue wave can be reduced to the corresponding rogue wave of the nonlinear Schrödinger equation under a suitable parametric condition.