Long-time evolution of pulses in the Korteweg-de Vries equation in the absence of solitons reexamined: Whitham method.
basic_science · Level V
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- Also identified by DOI 10.1103/PhysRevE.99.012210.
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Abstract
We consider the long-time evolution of pulses in the Korteweg-de Vries equation theory for initial distributions which produce no soliton but instead lead to the formation of a dispersive shock wave and of a rarefaction wave. An approach based on Whitham modulation theory makes it possible to obtain an analytic description of the structure and to describe its self-similar behavior near the soliton edge of the shock. The results are compared with numerical simulations.