Unified approach to Miura, Bäcklund and Darboux Transformations for Nonlinear Partial Differential Equations

DOI

10.2991/jnmp.1998.5.1.8How to use a DOI?

Abstract

This paper is an attempt to present and discuss at some length the Singular Manifold Method. This Method is based upon the Painlevé Property systematically used as a tool for obtaining clear cut answers to almost all the questions related with Nonlinear Partial Differential Equations: Lax pairs, Miura, Bäcklund or Darboux Transformations as well as -functions, in a unified way. Besides to present the basics of the Method we exemplify this approach by applying it to four equations in (1 + 1)-dimensions. Two of them are related with the other two through Miura transformations that are also derived by using the Singular Manifold Method.

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  - P.G. Estévez
AU  - E. Conde
AU  - P.R. Gordoa
PY  - 1998
DA  - 1998/02/01
TI  - Unified approach to Miura, Bäcklund and Darboux Transformations for Nonlinear Partial Differential Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 82
EP  - 114
VL  - 5
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1998.5.1.8
DO  - 10.2991/jnmp.1998.5.1.8
ID  - Estévez1998
ER  -