Whitham equations and phase shifts for the Korteweg-deVries equation
Mark J. Ablowitz, Justin T. Cole, Igor Rumanov
TL;DR
This paper develops higher-order Whitham theory for the semi-classical Korteweg-deVries equation with step-like data, providing detailed phase and solution analysis confirmed by numerical validation.
Contribution
It introduces higher-order perturbation analysis in Whitham theory for the Korteweg-deVries equation, advancing understanding of phase shifts and solutions.
Findings
Higher-order Whitham theory constructed for the semi-classical KdV
Explicit phase and leading order solutions obtained
Numerical calculations confirm theoretical results
Abstract
The semi-classical Korteweg-deVries equation for step-like data is considered with a small parameter in front of the highest derivative. Using perturbation analysis Whitham theory is constructed to higher order. This allows the order one phase and the complete leading order solution to be obtained; the results are confirmed by extensive numerical calculations.
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