We apply the algebraic-geometric techniques developed for the study of mappings which have the singularity confinement property to mappings which are integrable through linearization. The main difference with respect to the previous studies is tha...
DIRECT AND INVERSE METHODS IN NONLINEAR EVOLUTION EQUATIONS 632(No.632) 171-222 2003年
The bilinear method introduced by Hirota to obtain exact solutions for nonlinear evolution equations is discussed. Firstly, several examples including the Korteweg-deVries, nonlinear Schrodinger and Toda equations are given to show how solutions a...
S Isojima   R Willox   J Satsuma   
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL 35(32) 6893-6909 2002年8月
The coupled KP (cKP) equation possesses N-soliton solutions with many more degrees of freedom than the solitons for the usual KP equation have. In comparison, cKP solutions can therefore be expected to model far more complex interactions than thei...
A Nobe   J Satsuma   T Tokihiro   
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS 18(2) 293-305 2001年6月
We construct a difference equation which preserves any time evolution pattern of the rule 90 elementary cellular automaton. We also demonstrate that such difference equations can be obtained for any elementary cellular automata.
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...