Bilinear Equations and Bäcklund Transformation for Generalized Ultradiscrete Soliton Solution

Details Bilinear Equations and Bäcklund Transformation for Generalized Ultradiscrete Soliton Solution Bilinear Equations and Bäcklund Transformation for Generalized Ultradiscrete Soliton Solution

2010-03-10

arxiv.org/abs/1003.2016v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

11 pages

Scientific paper

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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