N. Mimura   J. Satsuma   A. Ramani   B. Grammaticos   
Journal of Mathematical Physics 54(2) 23504 2013年2月
We present the singularity analysis of the ultradiscrete analogue of linearisable mappings of Quispel-Roberts-Thompson (QRT) type. The ultradiscretisation method used here is one which keeps track of signs and thus can be applied without the posit...
A. Ramani   B. Grammaticos   J. Satsuma   
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 45(36) 365202-365202 2012年9月
We examine a class of second-order mappings which can be integrated by reduction to a linear equation. These mappings have been identified in our previous works where we have precisely shown how to obtain their linearization. The mappings belongin...
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 45(15) No.15 2012年4月
Ultradiscrete Ai and Bi functions are directly derived through the ultradiscrete limit from q-difference analogues of the Ai and Bi functions, respectively. An infinite number of identities among the number of restricted partitions are obtained as...
JOURNAL OF MATHEMATICAL PHYSICS 53(2) 023510-023510 2012年2月
Ultradiscrete singularity confinement test, which is an integrability detector for ultradiscrete equations with parity variables, is applied to various ultradiscrete equations. The ultradiscrete equations exhibit singularity structures analogous t...
A. Ramani   B. Grammaticos   J. Satsuma   R. Willox   
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 41(20) 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...