1. An Ultradiscrete Matrix Version of the Fourth Painlevé Equation.
- Author
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Field, Chris M. and Ormerod, Chris M.
- Subjects
- *
PAINLEVE equations , *MATRICES (Mathematics) , *NONLINEAR differential equations , *DIFFERENCE equations , *NONLINEAR theories - Abstract
This paper is concerned with the matrix generalization of ultradiscrete systems. Specifically, we establish a matrix generalization of the ultradiscrete fourth Painlevé equation (ud-PIV). Well-defined multicomponent systems that permit ultradiscretization are obtained using an approach that relies on a group defined by constraints imposed by the requirement of a consistent evolution of the systems. The ultradiscrete limit of these systems yields coupled multicomponent ultradiscrete systems that generalize ud-PIV. The dynamics, irreducibility, and integrability of the matrix-valued ultradiscrete systems are studied. [ABSTRACT FROM AUTHOR]
- Published
- 2007
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