Soliton solutions and Bäcklund transformation for the normalized linearly coupled nonlinear wave equations with symbolic computation

Under investigation in this paper are the normalized linearly coupled nonlinear wave equations, which can be used to describe the pulse propagation in the two-core optical fiber. Based on the Hirota's method and symbolic computation, the bilinear form and soliton solutions for the equations are derived. Furthermore, Bäcklund transformation (BT) in bilinear forms is given. Through the BT, a type of solutions and Lax pair are derived under certain conditions. Propagation characteristics and interaction behaviors of the solitons are discussed through the graphical analysis. Results of this paper might be helpful for the future development of some optical devices used in the modern optical communication systems, such as the directional couplers, polarization splitters, interferometers and modulators.