On the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data II. Perturbations with Finite Moments

TL;DR

This paper addresses solving the Korteweg-de Vries equation's initial value problem with steplike finite-gap data, focusing on perturbations that have finite moments and derivatives, advancing understanding of such complex initial conditions.

Contribution

It introduces a method to solve the Korteweg-de Vries equation with steplike finite-gap initial data under finite moment perturbations, extending previous results to more general initial conditions.

Findings

Established existence of solutions for steplike finite-gap initial data.

Extended analytical techniques to handle perturbations with finite moments.

Provided conditions under which solutions to the Korteweg-de Vries equation exist.

Abstract

We solve the Cauchy problem for the Korteweg-de Vries equation with steplike quasi-periodic, finite-gap initial conditions under the assumption that the perturbations have a given number of derivatives with finite moments.