Table of Contents
International Journal of Partial Differential Equations
Volume 2014 (2014), Article ID 830413, 10 pages
http://dx.doi.org/10.1155/2014/830413
Research Article

On Construction of Solutions of Evolutionary Nonlinear Schrödinger Equation

SunEdison, 501 Pearl Drive, St. Peters, MO 63376, USA

Received 1 May 2014; Accepted 30 June 2014; Published 7 October 2014

Academic Editor: Nikolai A. Kudryashov

Copyright © 2014 Andrey Melnikov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this work we present an application of a theory of vessels to a solution of the evolutionary nonlinear Schrödinger (NLS) equation. The classes of functions for which the initial value problem is solvable rely on the existence of an analogue of the inverse scattering theory for the usual NLS equation. This approach is similar to the classical approach of Zakharov-Shabath for solving evolutionary NLS equation but has an advantage of simpler formulas and new techniques and notions to understand the solutions.