New Integrable Coupled Nonlinear Schrödinger Equations

Faculty of Mathematics and Natural Sciences, Department of Theoretical Physics, Theoretical and Computational Physics Lab., Pattimura University, Ambon, Indonesia ABSTRACT Two types of integrable coupled nonlinear Schrödinger (NLS) equations are derived by using Zakharov-Shabat (ZS) dressing method.The Lax pairs for the coupled NLS equations are also investigated using the ZS dressing method. These give new types of the integrable coupled NLS equations with certain additional terms. Then, the exact solutions of the new types are obtained. We find that the solution of these new types do not always produce a soliton solution even they are the kind of the integrable NLS equations.