Stability and symmetry of solitary-wave solutions to systems modeling interactions of long waves

We consider systems of equations which arise in modelling strong interactio ns of weakly nonlinear long waves in dispersive media. For a certain class of such systems, we prove the existence and stability of localized solution s representing coupled solitary waves travelling at a common speed. Our res ults apply in particular to the systems derived by Gear and Grimshaw and by Liu, Kubota and Ko as models for interacting gravity waves in a density-st ratified fluid, For the latter system, we also prove that any coupled solit ary-wave solution must have components which are all symmetric about a comm on vertical axis. (C) 2000 Editions scientifiques et medicales Elsevier SAS .