Journal of Nonlinear Mathematical Physics

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...

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...

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....

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...

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...