JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 44(17) 175201-175201 2011年4月
Ultradiscretization with parity variables, which keeps the information of original variables' sign, is applied to the q-Painleve II equation of type A(6) (q-PII). A special solution of the resulting ultradiscrete system, which corresponds to ...
We apply a method that we have already proposed for the systematic discretisation of differential systems to the construction of discrete analogues of the Painleve equations. The important point is that in the case of the Painleve equations one ne...
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...