Long-time evolution of pulses in the Korteweg-de Vries equation in the absence of solitons revisited: Whitham method

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.

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Cited by in corpus (5)

• Quantitative Analysis of Shock Wave Dynamics in a Fluid of Light
• Wave breaking and formation of dispersive shock waves in a defocusing nonlinear optical material
• Evolution of wave pulses in fully nonlinear shallow-water theory
• Propagation of wave packets along intensive simple waves
• Non-linear edge dynamics of an Integer Quantum Hall fluid