Journal of Nonlinear Mathematical Physics

Volume 15, Issue 4, December 2008

1. Contiguity relations for discrete and ultradiscrete Painleve equations

A Ramani, B. Grammaticos, R. Willox
Pages: 353 - 364
We show that the solutions of ultradiscrete Painleve equations satisfy contiguity relations just as their continuous and discrete counterparts. Our starting point are the relations for q-discrete Painleve equations which we then proceed to ultradiscretise. In this paper we obtain results for the one-parameter...

2. Solutions of some second order ODEs by the extended Prelle-Singer method and symmetries

A. Ghose Choudhury, Partha Guha, Barun Khanra
Pages: 365 - 382
In this paper we compute first integrals of nonlinear ordinary differential equations using the extended Prelle-Singer method, as formulated by Chandrasekar et al in J. Math. Phys. 47 (2), 023508, (2006). We find a new first integral for the Painlev´e-Gambier XXII equation. We also derive the first integrals...

3. Symmetry analysis for Whitham-Broer-Kaup equations

Zhiyong Zhang, Xuelin Yong, Yufu Chen
Pages: 383 - 397
We investigate a further group analysis of Whitham-Broer-Kaup(for short WBK) equations. An optimal system of one-dimensional subalgebras is derived and used to construct reduced equations and similarity solutions. Moreover, a special case of WBK equations is linearized and some new solutions are obtained....

4. Doubly periodic waves of a discrete nonlinear Schrodinger system with saturable nonlinearity

Robert Conte, K. W. Chow
Pages: 398 - 409
A system of two discrete nonlinear Schr¨odinger equations of the Ablowitz-Ladik type with a saturable nonlinearity is shown to admit a doubly periodic wave, whose long wave limit is also derived. As a by-product, several new solutions of the elliptic type are provided for NLS-type discrete and continuous...

5. Asymptotically isochronous systems

Francesco Calogero, David Gomez-Ullate
Pages: 410 - 426
Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent variables tend asymptotically to functions periodic with the same fixed period. We focus on two such mechanisms, emphasizing...