Institute of Mathematics for Industry

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Ultradiscrete Allen-Cahn equation


Hold Date 2011-10-06 15:30~2011-10-06 17:00

Place Seminar Room 3, Faculty of Mathematics building, Ito Campus

Object person  

Speaker Mikio MURATA (Aoyama Gakuin University)

Abstract:
Ultradiscretization is a limiting procedure transforming a given difference equation into a cellular automaton. In addition the cellular automaton constructed by this procedure preserves the essential properties of the original equation, such as the structure of exact solutions. We present a systematic approach to the construction of ultradiscrete analogues for differential systems. Our method is tailored to first-order differential equations and reaction-diffusion systems. We apply our method to Allen-Cahn equation which is the well-known one-component reaction-diffusion equation.

Because ultradiscrete equations are piecewise linear equations, various exact solutions can be obtained from the `linearity'. Stationary solutions, travelling wave solutions and entire solutions of the resulting ultradiscrete systems are constructed. These solutions are similar to the solutions of the original equation.


This seminar is combined with Integrable Systems Seminar.