Wronskian solutions to the KdV equation via B\"acklund transformation
Qi-fei Xuan, Mei-ying Ou, Da-jun Zhang
TL;DR
This paper explores how Wronskian solutions to the KdV equation can be systematically generated using Bäcklund transformations, linking various solution types through specific conditions on Wronskian entries.
Contribution
It introduces a method to derive transformations between different solution types of the KdV equation using Wronskian entries and Bäcklund transformations.
Findings
Derived conditions for Wronskian entries in Bäcklund transformations
Established transformations between solitons, negatons, positons, rational solutions, and complexitons
Provided a systematic approach to generate diverse solutions of the KdV equation
Abstract
In the paper we discuss the B\"acklund 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 B\"acklund transformation of the KdV equation. By choosing suitable Wronskian entries and the parameter in the bilinear B\"acklund transformation, we obtain transformations between many kinds of solutions.
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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Advanced Differential Equations and Dynamical Systems