Soliton solutions for coupled nonlinear Schrödinger equations with linear self and cross coupling terms

In this paper, coupled nonlinear Schrödinger equations with linear self and cross coupling terms are investigated analytically. We obtain the exact soliton solutions which exist a periodic-wave background for this system, including one-, two- and N-soliton solutions. We find the period of oscillation for periodic wave background is related to the coupling terms. In addition, by adjusting other parameters we can get many types of mixed soliton solutions on the plane-wave background. Moreover, the interactions of the two and three solitons have been discussed through a detailed analysis for the asymptotic behavior and it displays that they are all elastic.