Exact solutions for a perturbed nonlinear Schrödinger equation by using Bäcklund transformations

✍ Scribed by Hassan A. Zedan; Seham Sh. Tantawy

• Publisher: John Wiley and Sons
• Year: 2009
• Tongue: English
• Weight: 105 KB
• Volume: 32
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1076

✦ Synopsis

Abstract

In this paper, the method of deriving the Bäcklund transformation from the Riccati form of inverse method is presented for the perturbed nonlinear Schrödinger equation (PNSE). Consequently, the exact solutions for the PNSE can be obtained by the AKNS class. The technique developed relies on the construction of the wave functions that are solutions of the associated AKNS, that is, a linear eigenvalues problem in the form of a system of partial differential equation. Moreover, we construct a new soliton solution from the old one and its wave function. Copyright © 2008 John Wiley & Sons, Ltd.