Bilinear Equations and B\"acklund Transformation for Generalized Ultradiscrete Soliton Solution
Exactly Solvable and Integrable Systems
2015-05-18 v1
Abstract
Ultradiscrete soliton equations and B\"acklund transformation for a generalized soliton solution are presented. The equations include the ultradiscrete KdV equation or the ultradiscrete Toda equation in a special case. We also express the solution by the ultradiscrete permanent, which is defined by ultradiscretizing the signature-free determinant, that is, the permanent. Moreover, we discuss a relation between B\"acklund transformations for discrete and ultradiscrete KdV equations.
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Cite
@article{arxiv.1003.2016,
title = {Bilinear Equations and B\"acklund Transformation for Generalized Ultradiscrete Soliton Solution},
author = {Hidetomo Nagai and Daisuke Takahashi},
journal= {arXiv preprint arXiv:1003.2016},
year = {2015}
}
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11 pages