On two-parameter solutions of simultaneous ultradiscrete Painleve II equation with parity variables

Abstract

We introduce a simultaneous ultradiscrete Painleve II equation with parity variables, which is shown to be more suitable for studying two-parameter solutions than the single second-order ultradiscrete Painleve II equation with parity variables. We investigate several types of two-parameter solutions and the solutions which are related with the ultradiscrete limit of determinant type solutions of q-Painleve II equation.

39 pages, title changed, figures added, typos corrected

References in corpus (2)

• Exact Solutions with Two Parameters for an Ultradiscrete Painlevé Equation of Type $A_6^{(1)}$
• A Class of Special Solutions for the Ultradiscrete Painlevé II Equation

Cited by in corpus (1)

• Polynomial solutions of $q$-Heun equation and ultradiscrete limit