Unified approach to Miura, B\"acklund and Darboux transformations for nonlinear partial differential equations
Estévez, P. G. ; Conde, Esther ; Gordoa, Pilar R.
arXiv, 9801207 / Harvested from arXiv
Text on arXiv
This paper is an attempt to present and discuss at some length the Singular Manifold Method. This Method is based upon the Painlev\'e 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, B\"acklund or Darboux Transformations as well as $\tau$-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.
Publié le : 1997-12-31
Classification:  Mathematical Physics,  Mathematics - Analysis of PDEs 
@article{9801207,
     author = {Est\'evez, P. G. and Conde, Esther and Gordoa, Pilar R.},
     title = {Unified approach to Miura, B\"acklund and Darboux transformations for
  nonlinear partial differential equations},
     journal = {arXiv},
     volume = {1997},
     number = {0},
     year = {1997},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9801207}
}

Estévez, P. G.; Conde, Esther; Gordoa, Pilar R. Unified approach to Miura, B\"acklund and Darboux transformations for
  nonlinear partial differential equations. arXiv, Tome 1997 (1997) no. 0, . http://gdmltest.u-ga.fr/item/9801207/