Analysis of a coupled short pulse system via symmetry method

Abstract

In this paper, we focus on two different points. Firstly, the Lie symmetry analysis is presented for a coupled short pulse system which describes the propagation of two orthogonally polarized modes in optical fibers. Then the similarity reductions and exact solutions of the system are performed based on the optimal systems. Secondly, the explicit solutions are constructed by the power series method. Moreover, the convergence of the power series solutions are discussed. Such power series solutions and similarity reductions are important in both applications and the theory of nonlinear waves.