Journal of Nonlinear Mathematical Physics

Volume 2, Issue 3-4, September 1995, Pages 398 - 404

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

Authors
Shunji KAWAMOTO
Corresponding Author
Shunji KAWAMOTO
Available Online 19 December 2006.
DOI
https://doi.org/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.
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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
2 - 3
Pages
398 - 404
Publication Date
2006/12
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.2991/jnmp.1995.2.3-4.20How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - JOUR
AU  - Shunji KAWAMOTO
PY  - 2006
DA  - 2006/12
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  - https://doi.org/10.2991/jnmp.1995.2.3-4.20
ID  - KAWAMOTO2006
ER  -