Novel rogue waves in an inhomogenous nonlinear medium with external potentials

•The vcNLSE with external potentials is studied by the similarity transformation.•Two types of analytical rogue wave solutions for this equation are obtained.•Abundant structures of rogue waves are constructed through these solutions.•The main properties and the dynamic behaviors of these rogue waves are discussed.

Employing the similarity transformation connected with the standard constant coefficient nonlinear Schrödinger equation, we obtain the analytical rogue wave solutions to a generalized variable coefficient nonlinear Schrödinger equation with external potentials describing the pulse propagation in nonlinear media with transverse and longitudinal directions nonuniformly distributed. Based on the obtained solutions, abundant structures of rogue waves are constructed by selecting some special parameters. The main properties as well as the dynamic behaviors of these rogue waves are discussed by direct computer simulations.