The Research Of The Solutions In Coupled Nonlinear Schr(o|")dinger Equations With Variable Coefficients

This paper focus on the study of the solutions of the coupled nonlinear Schrodinger equations with variable coefficients. Frist, the designable integrability method was constructed, which built up the relationship between the coupled nonlinear Schrodinger equations with variable coefficients and the classical coupled nonlinear Schrodinger equations. Then, the solutions of the classical coupled nonlinear Schrodinger equations were worked out by Darboux transformation. Furthermore, we could get the Bright-Bright solitons, Bright-Dark solitons and rogue wave solutions of the coupled nonlinear Schrodinger equations with variable coefficients. Finally, we studied the change of the solutions of the equations under the designable optical super-lattice potentials and hyperbolic cosine potentials with parameters, which are two kinds of important potentials in physics. In conclusion, this method might be used to design a large variety of external potentials in the coupled nonlinear Schrodinger equations with variable coefficients, which are important for the research of the soultions to the integrable system.