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First order compatibility of the Cubic Schrodinger equation
by
Daniel J. Arrigo
University of Central Arkansas
Coauthors: David A. Ekrut and Jackson R. Fliss
In this talk we consider the compatibility between the nonlinear Cubic Schrodinger equation and a general quasilinear system of partial differential equations (PDEs). Recently it has been proven that the compatibility between PDEs and their associated invariant surface condition recovers the nonclassical method of symmetry reduction. This can be seen as a generalization of that method. Here we show that two classes of compatible equation exist. The first recovers the results obtainable by the classical symmetry method whereas the second is an entirely new class of compatible equation. We solve this in conjunction with the original system leading to a new reduction of the Cubic Schrodinger equation.
Date received: September 14, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caww-31.