Asymptotics of the first correction in the perturbation of theN-soliton solution to the KdV equation

Abstract

We consider a triple Fourier-type integral that represents a solution to the KdV equation linearized on anN-soliton potential. Assuming that the parameters of the potential depend on the slow timeet, we construct an asymptotics of this integral ase → 0 uniform with respect tox, t up to large timet ∼ e−1.