arXiv subjects

J. Satsuma

Publications and source records attributed to J. Satsuma.

4 recordsLinked to original sources

arXiv2002

The space of initial conditions for linearisable mappings

We apply the algebraic-geometric techniques developed for the study of mappings which have the singularity confinement property to mappings which are integrable through linearisation. The main difference with respect to the previous studies is that the linearisable mappings have generically unconfined singularities. Despite this fact we are able to provide a complete description of the dynamics of these mappings and derive rigorously their growth properties.

nlin.SI↗

arXiv1997

Two-dimensional soliton cellular automaton of deautonomized Toda-type

A deautonomized version of the two-dimensional Toda lattice equation is presented. Its ultra-discrete analogue and soliton solutions are also discussed.

solv-int↗

arXiv1994

Bilinear Discrete Painleve-II and its Particular Solutions

By analogy to the continuous Painlevé II equation, we present particular solutions of the discrete Painlevé II (d-P$\rm_{II}$) equation. These solutions are of rational and special function (Airy) type. Our analysis is based on the bilinear formalism that allows us to obtain the $τ$ function for d-P$\rm_{II}$. Two different forms of bilinear d-P$\rm_{II}$ are obtained and we show that they can be related by a simple gauge transformation.

solv-int↗

arXiv1994

Bilinear Structure and Exact Solutions of the Discrete Painlevé I Equation

Bilinear structure for the discrete Painlevé I equation is investigated. The solution on semi-infinite lattice is given in terms of the Casorati determinant of discrete Airy function. Based on this fact, the discrete Painlevé I equation is naturally extended to a discrete coupled system. Corresponding matrix model is also mentioned.

solv-int↗