Asymptotic solitons of the modified Korteweg-de Vries equation

Abstract

The paper considers the Cauchy problem for the equation upsilon t+6 upsilon 2 upsilon x+ upsilon xxx=0 with step-like initial data. It is proved by the inverse scattering method that for t to infinity the solution upsilon (x,t) in the neighbourhood of the leading edge breaks up into an infinite series of non-interacting solitons generated by the continuous spectrum of the respective L operator of the Lax representation.