Wronskian solutions to the KdV equation via B\"acklund transformation
Exactly Solvable and Integrable Systems
2007-06-26 v1
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.
Keywords
Cite
@article{arxiv.0706.3487,
title = {Wronskian solutions to the KdV equation via B\"acklund transformation},
author = {Qi-fei Xuan and Mei-ying Ou and Da-jun Zhang},
journal= {arXiv preprint arXiv:0706.3487},
year = {2007}
}
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16 pages