Periodic oscillations and nonlinear tunneling of soliton for Hirota-MB equation in inhomogeneous fiber

Abstract

Under investigation in this paper is an inhomogeneous Hirota-Maxwell Bloch equation, which describes the propagation of optical soliton inhomogeneous fiber. For considered equation, corresponding Lax pair is constructed. Via the Darboux transformation method and symbolic computation, one and two soliton solutions are attained. For obtained one soliton solution, nonlinear tunneling of soliton through dispersion barrier on exponential background have been discussed. Using obtained two soliton solutions, periodic oscillation of solitons and their interactions are studied. Especially, soliton fission from the merged two solitons is observed which can be used to construct the soliton based ultrafast switching. Influence of the variable coefficients and erbium on the soliton solutions are analyzed. By keeping third order dispersion as periodic function and other coefficients are consider as constants, collision less propagation also have been discussed. We hope that our analytical results will be helpful to understand the soliton tunneling and periodic oscillation in an inhomogeneous erbium doped fiber experimentally.