Stability and symmetry of solitary-wave solutions to systems modeling interactions of long waves (Q1569021)

The authors consider systems of equations which arise in modelling strong interactions of weakly nonlinear long waves in dispersive media. For a certain class of such systems, they prove the existence and stability of localized solutions representing coupled solitary waves travelling at a common speed. The presented results 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-stratified fluid. For the latter system, it is proved that any coupled solitary-wave solution must have components which are all symmetric about a common vertical axis.