The Bäcklund and the Galilei Invariant Transformations Constructed by Similarity Variables for Soliton Equations

DOI

10.2991/jnmp.1995.2.3-4.20How to use a DOI?

Abstract

The Painlevé-test has been applied to checking the integrability of nonlinear PDEs, since similarity solutions of many soliton equations satisfy the Painlevé equation. As is well known, such similarity solutions can be obtained by the infinitesimal transformation, that is, the classical similarity analysis, and also the dimension of the PDEs can be reduced. In this paper, the KdV, the mKdV, and the nonlinear Schrödinger equations are considered and are transformed into equations with loss and/or nonuniformity by transformations constructed on a basis of the local similarity variables. The transformations include the Bäcklund and the Galilei invariant ones. It should be noticed that the approach is applicable to other PDEs and for nonlocal similarity variables.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Shunji Kawamoto
PY  - 1995
DA  - 1995/09/01
TI  - The Bäcklund and the Galilei Invariant Transformations Constructed by Similarity Variables for Soliton Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 398
EP  - 404
VL  - 2
IS  - 3-4
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1995.2.3-4.20
DO  - 10.2991/jnmp.1995.2.3-4.20
ID  - Kawamoto1995
ER  -