Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2010-03-10
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.
Nagai Hidetomo
Takahashi Daisuke
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