FIRST-ORDER PERTURBED KORTEWEG-DE-VRIES SOLITONS

We consider the Korteweg-de Vries equation with a perturbation arising naturally in many physical situations. Although being asymptotically integrable, we show that the corresponding perturbed solitons do not h ave the usual scattering properties. Specifically, we show that there is a solution, correct up to O(epsilon), where epsilon is the perturba tive parameter, consisting, at t-->-infinity, of two superposed deform ed solitons characterized by wave numbers k(1) and k(2) that give rise , for t-->+infinity, to the same but phase-shifted superposed solitons plus a coupling term depending on k(1) and k(2). We also find the con dition on the original equation for which this coupling vanishes.