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

M. Isoard ¹ A. M. Kamchatnov ² N. Pavloff ¹

Physical Review E , American Physical Society (APS), 2019, 〈10.07952〉

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.

• 1. LPTMS – Laboratoire de Physique Théorique et Modèles Statistiques
• 2. Institute of Spectroscopy