WEAKLY NONLOCAL SOLITARY WAVES IN A SINGULARLY PERTURBED KORTEWEG-DEVRIES EQUATION

A fifth-order Korteweg-de Vries equation is considered, where the fift h-order derivative term is multiplied by a small parameter. It is know n that solitary wave solutions of this model equation are nonlocal in that the central core of the wave is accompanied by copropagating trai ling oscillations. Here, using the techniques of exponential asymptoti cs, these solutions are reexamined and it is established that they for m a one-parameter family characterized by the phase shift of the trail ing oscillations. Explicit asymptotic formula relating the oscillation amplitude to the phase shift are obtained.