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Unified approach to Miura, B\"acklund and Darboux transformations for nonlinear partial differential equations

P. G. Estévez·Esther Conde·Pilar R. Gordoa
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Abstract

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.

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P. G. Estévez, Esther Conde, Pilar R. Gordoa. 1998-01-01. Unified approach to Miura, B\"acklund and Darboux transformations for nonlinear partial differential equations. https://doi.org/10.2991/jnmp.1998.5.1.8

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