Bilinear Equations and Bäcklund Transformation for Generalized Ultradiscrete Soliton Solution

Abstract

Ultradiscrete soliton equations and Bäcklund 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 Bäcklund transformations for discrete and ultradiscrete KdV equations.

11 pages

References in corpus (2)

• The Baecklund transformation equations for the ultradiscrete KP equation
• A New Expression of Soliton Solution to the Ultradiscrete Toda Equation

Cited by in corpus (3)

• Solutions to the ultradiscrete Toda molecule equation expressed as minimum weight flows of planar graphs
• Solutions to the ultradiscrete KP hierarchy and its reductions
• Solutions to the ultradiscrete KdV equation expressed as the maximum of a quadratic function