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...
Exact solutions of the ultradiscrete Sine-Gordon equation which have oscillating structure are constructed. They are considered to be a counterpart of the breather solution of the Sine-Gordon equation. They are given by setting specific parameters...
A. Ramani   B. Grammaticos   J. Satsuma   R. Willox   
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 41(20) 205204-205204 2008年5月
We show that a discretization of a continuous system may entail 'hidden' delays and thus introduce instabilities. In this case, while the continuous system has an attractive fixed point, the instabilities present in the equivalent discre...
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...