S. Isojima   S. Kubo   M. Murata   J. Satsuma   
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 41(2) 025205 2008年1月
The Backlund transformation for the discrete Korteweg-de Vries equation is introduced in the bilinear form. The superposition formula is also derived from the transformation. An ultradiscrete analogue of the transformation is presented by means of...
R. Willox   A. Ramani   J. Satsuma   B. Grammaticos   
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 385(2) 473-486 2007年11月
We examine the transition between discrete and ultradiscrete (cellular-automaton-like) systems, the dynamics of which exhibit limit cycles. Motivated by results obtained previously for three-dimensional systems, we consider here a more manageable ...
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 40(42) 12619-12627 2007年10月
We construct special solutions of the Hirota-Miwa equation for which the tau-function is a polynomial in the independent variables. Three different methods are presented: direct construction ( obtained also as a limit of the soliton solutions), an...
S. Kubo   S. Isojima   M. Murata   J. Satsuma   
PHYSICS LETTERS A 362(5-6) 430-434 2007年3月
An ultradiscrete analogue of the Miura transformation is constructed through the bilinear form of the discrete KdV and modified KdV equations. This transformation maps solutions of the 'box and ball system with a carrier' to those of the 'box and ...
S. Isojima   M. Murata   A. Nobe   J. Satsuma   
PHYSICS LETTERS A 357(1) 31-35 2006年8月
The discrete modified Korteweg-de Vries equation admits exact solutions with nondefinite sign, which describe interaction among solitons with positive and negative amplitude. In this Letter a transformation of hyperbolic sine type is proposed in o...
M. Murata   J. Satsuma   A. Ramani   B. Grammaticos   
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 43(31) 2010年8月
We present a systematic approach to the construction of discrete analogues for differential systems. Our method is tailored to first-order differential equations and relies on a formal linearization, followed by a Pade-like rational approximation ...
A. Ramani   B. Grammaticos   J. Satsuma   R. Willox   
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 42(28) 282002 2009年7月
We examine two integrable discrete lattice equations obtained by Levi and Yamilov. We show that the first one is a form of the lattice KdV equation already obtained by Hirota and Tsujimoto, while the second one is a discrete form of mKdV. We prese...
A. Ramani   B. Grammaticos   J. Satsuma   R. Willox   
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 42(28) 282002 2009年7月
We examine two integrable discrete lattice equations obtained by Levi and Yamilov. We show that the first one is a form of the lattice KdV equation already obtained by Hirota and Tsujimoto, while the second one is a discrete form of mKdV. We prese...
A. Ramani   B. Grammaticos   J. Satsuma   
CHAOS SOLITONS & FRACTALS 40(1) 491-496 2009年4月
We present two models for an epidemic where the individuals are infective over it fixed period of time and which never becomes endemic i.e., no infective individuals remain after the epidemic has run its course. The first model is based oil it del...
A. Ramani   B. Grammaticos   J. Satsuma   
CHAOS SOLITONS & FRACTALS 40(1) 491-496 2009年4月
We present two models for an epidemic where the individuals are infective over it fixed period of time and which never becomes endemic i.e., no infective individuals remain after the epidemic has run its course. The first model is based oil it del...