2007•arXiv (Cornell University)Open access

Wronskian solutions to the KdV equation via Bäcklund transformation

Xuan Qi-Fei, Ou Mei-Ying, Da‐jun Zhang

Abstract

In the paper we discuss the Bäcklund transformation of the KdV equation between solitons and solitons, between negatons and negatons, between positons and positons, between rational solution and rational solution, and between complexitons and complexitons. We investigate the conditions that Wronskian entries satisfy for the bilinear Bäcklund transformation of the KdV equation. By choosing suitable Wronskian entries and the parameter in the bilinear Bäcklund transformation, we obtain transformations between many kinds of solutions.

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Key concepts: Wronskian, Korteweg–de Vries equation, Transformation (genetics), Mathematics, Applied mathematics, Mathematical economics, Mathematical physics, Physics