Abstract

Exact Solutions of the Nonlinear Schrodinger Equation with Certain Central

Z.Hassan (Department of Mathematics, Faculty of Education, University of Tanta, Kafr El-Sheikh, Egypt); A.A.Darwish (Department of Mathematics, Faculty of Science, Helwan University,Cairo, Egypt)

e-mail: zedanhassan@hotmail.com; Hassan-zedan@maktoob.com

We consider the family of nonlinear Schroedinger equation, which arise from the study of the nonlinear wave propagation in dispersive and inhomogeneous media. These equations arise in a wide range of plasma phenomena, in nonlinear and non-uniform dielectric medium, and in other fields of physics. Using the Darboux-Bargmann technique, we obtain the Backlund transformations for nonlinear Schrodinger equation solvable by the inverse-Scattering method and construct explicit solution and the BT technique is used to generate a new solution of NLSE from a known solution of the equation. Reference 1-H.Chen and C.S.Liu, Soliton in nonuniform media ,phys.Rev. Lett.,37,693-697(1974) 2- Hassan A. Zedan, Group Classification of a Heterogeneous Schrodinger Equations, Int. J. Non-Linear Mech., 30,4,479-485,1995 3- Ablowitzm,J and P.A. Clarkson, Solitons, nonlinear Evalution Equations and Inverse Scattering, Cambridge University press,Cambridge, 1991 4-Rogers C. and Shadwick w.E., Backlund Transformations and their Applications, Academic press, New York, 1982

Section : 12