Unified approach to Miura, Bäcklund and Darboux Transformations for Nonlinear Partial Differential Equations
- 10.2991/jnmp.19220.127.116.11How to use a DOI?
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.
- © 2006, the Authors. Published by Atlantis Press.
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- This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
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.1918.104.22.168 DO - 10.2991/jnmp.1922.214.171.124 ID - Estévez1998 ER -