Propagation of wave packets along intensive simple waves
arXiv:2103.07643 · doi:10.1063/5.0050618
Abstract
We consider propagation of high-frequency wave packets along a smooth evolving background flow whose evolution is described by a simple-wave type of solutions of hydrodynamic equations. In geometrical optics approximation, the motion of the wave packet obeys the Hamilton equations with the dispersion law playing the role of the Hamiltonian. This Hamiltonian depends also on the amplitude of the background flow obeying the Hopf-like equation for the simple wave. The combined system of Hamilton and Hopf equations can be reduced to a single ordinary differential equation whose solution determines the value of the background amplitude at the location of the wave packet. This approach extends the results obtained in Ref.~\cite{ceh-19} for the rarefaction background flow to arbitrary simple-wave type background flows. The theory is illustrated by its application to waves obeying the KdV equation.
arXiv comment10 pages, 15 figures
References in corpus (8)
- Resolution of a shock in hyperbolic systems modified by weak dispersion
- Dispersive shock waves theory for non-integrable equations
- Gurevich-Pitaevskii problem and its development
- Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves
- Theory of quasi-simple dispersive shock waves and number of solitons evolved from a nonlinear pulse
- Evolution of wave pulses in fully nonlinear shallow-water theory
- Formation of dispersive shock waves in evolution of a two-temperature collisionless plasma
- Long-time evolution of pulses in the Korteweg-de Vries equation in the absence of solitons revisited: Whitham method
Cited by in corpus (6)
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- Asymptotic theory of not completely integrable soliton equations
- Propagation of wave packets along large-scale background waves
- Propagation of generalized Korteweg-de Vries solitons along large-scale waves
- Number of solitons produced from a large initial pulse in the generalized NLS dispersive hydrodynamics theory
- Shock waves in nonlinear transmission lines