In the long-wave, weakly nonlinear limit a generic model for the interaction of two waves with nearly coincident linear phase speeds is a pair of coupled Korteweg-de Vries equations. Here we consider the simplest case when the coupling occurs only through linear non-dispersive terms, and for...

We study the stability of a class of traveling waves in a model of weakly nonlinear water waves on the sphere. The model describes free surface potential flow of a fluid layer surrounding a gravitating sphere, and the evolution equations are Hamiltonian. For small amplitude oscillations the...

We discuss the evaluation of the stability, position and width of resonances in four-dimensional symplectic mappings. The approach presented in this paper is based on the computation of the resonant perturbative series carried out by the program ARES. This piece of code allows to perform the...