Theory of quasi-simple dispersive shock waves and number of solitons evolved from a nonlinear pulse

Abstract

The theory of motion of edges of dispersive shock waves generated after wave breaking of simple waves is developed. It is shown that this motion obeys Hamiltonian mechanics complemented by a Hopf-like equation for evolution of the background flow that interacts with edge wave packets or edge solitons. A conjecture about existence of a certain symmetry between equations for the small-amplitude and soliton edges is formulated. In case of localized simple wave pulses propagating through a quiescent medium this theory provided a new approach to derivation of an asymptotic formula for the number of solitons produced eventually from such a pulse.

arXiv comment9 pages, 2 figures

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• Quasiclassical integrability condition in AKNS scheme
• Propagation of dark solitons of DNLS equation along a large-scale background
• Number of solitons produced from a large initial pulse in the generalized NLS dispersive hydrodynamics theory
• Accessing and Manipulating Dispersive Shock Waves in a Nonlinear and Nonlocal Rydberg Medium
• Shock wave generation and propagation in dissipative and nonlocal nonlinear Rydberg media
• Modulation theory for the sine-Gordon equation