Superposition solitons for the mixed 4-coupled nonlinear Schrödinger equations

In this paper, the mixed 4-coupled nonlinear Schr & ouml;dinger equations with different nonlinear signs are studied to derive a new type of soliton solutions called the superposition soliton solutions. By using the Hirota method, we obtain the exact one-bright-three-superposition N-soliton solutions analytically. Notably, this kind of soliton solutions have not been researched in prior literature. Under certain conditions, the general mixed (bright-dark) soliton solutions can be obtained from our results such as all bright soliton solutions. In addition, the propagation characteristics, including elastic collision, time periodicity and soliton reaction, are displayed through graphic simulation. On this basis, the influence of various parameters on the phase, direction, and amplitude of soliton propogation is concluded. Finally, the asymptotic behaviors of 2, 3-soliton solutions are analyzed in detail.