37 citations · 75 across the 6 of their papers we have counts for
6 papers
Spatial pattern of discrete and ultradiscrete Gray-Scott model
Keisuke Matsuya, Mikio Murata
Ultradiscretization is a limiting procedure transforming a given difference equation into a cellular automaton. In addition the cellular automaton constructed by this procedure pre…
Exact Solutions with Two Parameters for an Ultradiscrete Painlevé Equation of Type
Mikio Murata
An ultradiscrete system corresponding to the -Painlevé equation of type , which is a -difference analogue of the second Painlevé equation, is proposed. Exact solut…
Lax forms of the -Painlevé equations
Mikio Murata
All -Painlevé equations which are obtained from the -analog of the sixth Painlevé equation are expressed in a Lax formalism. They are characterized by the data of the associa…
Two-component soliton systems and the Painlevé equations
Mikio Murata
We give an extension of the two-component KP hierarchy by considering additional time variables. We obtain the linear system by taking into consideration the hierarchy…
New Expressions for Discrete Painlevé Equations
Mikio Murata
It is known that discrete Painlevé equations have symmetries of the affine Weyl groups. In this paper we propose a new representation of discrete Painlevé equations in which the sy…
Riccati Solutions of Discrete Painlevé Equations with Weyl Group Symmetry of Type
Mikio Murata, Hidetaka Sakai, Jin Yoneda
We present a special solutions of the discrete Painlevé equations associated with , and -surface. These solutions can be expressed by solutions…