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Auto-Bäcklund transformation and similarity reductions for general variable coefficient KdV equations. (English) Zbl 0981.35064
Summary: Based on the idea of the homogeneous balance (HB) method, we study the Bäcklund transformation and similarity reductions of the general variable coefficient KdV equation. It is found that the corresponding results are coincide with those by the Weiss-Tabor-Carnevale (WTC) method and the Clarkson-Kruskal (CK) method, respectively. The close connections among the HB, WTC and CK methods are exposed in the theory. In the meantime, the Lax pair, symmetry, two conservation laws and a analytic solution for the general variable coefficient KdV equation are given.

35Q53KdV-like (Korteweg-de Vries) equations
37K35Lie-Bäcklund and other transformations
37K10Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
Full Text: DOI
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