Phase Shift in the Whitham Zone for the Gurevich-Pitaevskii Special Solution of the Korteweg-de Vries Equation

TL;DR

This paper derives the leading term of the Gurevich-Pitaevskii special solution to the KdV equation in the oscillation zone without relying on averaging methods, providing a new analytical approach.

Contribution

It introduces a novel method to obtain the leading term of the Gurevich-Pitaevskii solution without averaging, advancing analytical techniques for KdV solutions.

Findings

Derived the leading term explicitly

Avoided traditional averaging methods

Enhanced understanding of oscillation zone behavior

Abstract

We get the leading term of the Gurevich-Pitaevskii special solution to the KdV equation in the oscillation zone without using averaging methods.