Wronskian solutions to the KdV equation via Bäcklund transformation

2007/06/24 by Xuan Qi-Fei, Xuan, Qi-fei, Ou Mei-Ying +3
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0706.3487

openalex publication_date 2007/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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