Direct search for exact solutions to the nonlinear Schrödinger equation
نویسندگان
چکیده
A five-dimensional symmetry algebra consisting of Lie point symmetries is firstly computed for the nonlinear Schrödinger equation, which, together with a reflection invariance, generates two five-parameter solution groups. Three ansätze of transformations are secondly analyzed and used to construct exact solutions to the nonlinear Schrödinger equation. Various examples of exact solutions with constant, trigonometric function type, exponential function type and rational function amplitude are given upon careful analysis. A bifurcation phenomenon in the nonlinear Schrödinger equation is clearly exhibited during the solution process. 2009 Elsevier Inc. All rights reserved.
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عنوان ژورنال:
- Applied Mathematics and Computation
دوره 215 شماره
صفحات -
تاریخ انتشار 2009