Volume 2, Issue 3-4, September 1995, Pages 334 - 355
The Singular Manifold Method: Darboux Transformations and Nonclassical Symmetries
- P.G. ESTÉVEZ, P.R. GORDOA
- Corresponding Author
- P.G. ESTÉVEZ
Available Online 19 December 2006.
- https://doi.org/10.2991/jnmp.1995.2.3-4.14How to use a DOI?
- We present in this paper the singular manifold method (SMM) derived from Painlevé analysis, as a helpful tool to obtain much of the characteristic features of nonlinear partial differential equations. As is well known, it provides in an algorithmic way the Lax pair and the Bäcklund transformation for the PDE under scrutiny. Moreover, the use of singular manifold equations under homographic invariance consideration leads us to point out the connection between the SMM and socalled nonclassical symmetries as well as those obtained from direct methods. It is illustrated here by means of some examples. We introduce at the same time a new procedure that is able to determine the Darboux transformations. In this way, we obtain as a bonus the one and two soliton solutions at the same step of the iterative process to evaluate solutions.
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Cite this article
TY - JOUR AU - P.G. ESTÉVEZ AU - P.R. GORDOA PY - 2006 DA - 2006/12 TI - The Singular Manifold Method: Darboux Transformations and Nonclassical Symmetries JO - Journal of Nonlinear Mathematical Physics SP - 334 EP - 355 VL - 2 IS - 3-4 SN - 1776-0852 UR - https://doi.org/10.2991/jnmp.1995.2.3-4.14 DO - https://doi.org/10.2991/jnmp.1995.2.3-4.14 ID - ESTÉVEZ2006 ER -