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   Claassen, Kyle M. ; Johnson, Mathew A. ( August 2018 , Studies in Applied Mathematics)
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   The semi-classical Korteweg–de Vries 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 the 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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