Gurevich–Pitaevskii problem and its development

Камчатнов, А. М.

doi:10.3367/ufne.2020.08.038815

Cited by 22 publications

(5 citation statements)

References 111 publications

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“…17 (see also Ref. 18 and references therein). Solution of this equation with the initial condition k = k 0 at u = u 0 yields the dependence k = k(u) of the carrier wave number k on the value u of the background flow amplitude at the instant location of the packet.…”

Section: Discussionmentioning

confidence: 99%

Propagation of wave packets along intensive simple waves

Камчатнов

Shaykin

2021

Physics of Fluids

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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. 7 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.

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Section: Discussionmentioning

confidence: 99%

Propagation of wave packets along intensive simple waves

Камчатнов

Shaykin

2021

Physics of Fluids

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“…28 and 29). The small-amplitude edge propagates with the group velocity (11), that is during the time interval dt it moves to the distance dx = v g dt. Since this path lies on the surface u = u(x,t) of the dispersionless solution, the relation dx/dt = v g must be compatible with Eq.…”

Section: General Theorymentioning

confidence: 99%

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

Kamchatnov

2020

Preprint

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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.

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“…A general approach for describing DSWs in local nonlinear media was developed by Gurevich and Pitaevskii [51], which is based on the Whitham modulation theory of nonlinear waves [52,53]. In this approach, DSWs are approximated by modulated periodic-wave solutions, and the evolution of solution variables is governed by the Whitham modulation equations (see, e.g., [54][55][56][57] and review papers [58,59]). However, for systems with nonlocal Kerr nonlinearities, the nonlinear envelope equation will be modified into a nonlocal NLSE (NNLSE), which leads to significant consequences.…”

Section: Introductionmentioning

confidence: 99%

Accessing and manipulating dispersive shock waves in a nonlinear and nonlocal Rydberg medium

Hang

Bai

et al. 2023

Phys. Rev. A

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Dispersive shock waves (DSWs) are fascinating wave phenomena occurring in media when nonlinearity overwhelms dispersion (or diffraction). Creating DSWs with low generation power and realizing their active controls is desirable but remains a longstanding challenge. Here, we propose a scheme to generate weak-light DSWs and realize their manipulations in an atomic gas involving strongly interacting Rydberg states under the condition of electromagnetically induced transparency (EIT). We show that for a two-dimensional (2D) Rydberg gas a weak nonlocality of optical Kerr nonlinearity can significantly change the edge speed of DSWs, and induces a singular behavior of the edge speed and hence an instability of the DSWs. However, by increasing the degree of the Kerr nonlocality, the singular behavior of the edge speed and the instability of the DSWs can be suppressed. We also show that in a 3D Rydberg gas, DSWs can be created and propagate stably when the system works in the intermediate nonlocality regime. Due to the EIT effect and the giant nonlocal Kerr nonlinearity contributed by the Rydberg-Rydberg interaction, DSWs found here have extremely low generation power. In addition, an active control of DSWs can be realized; in particular, they can be stored and retrieved with high efficiency and fidelity through switching off and on a control laser field. The results reported here are useful not only for unveiling intriguing physics of DSWs but also for finding promising applications of nonlinear and nonlocal Rydberg media.

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Gurevich–Pitaevskii problem and its development

Cited by 22 publications

References 111 publications

Propagation of wave packets along intensive simple waves

Propagation of wave packets along intensive simple waves

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

Accessing and manipulating dispersive shock waves in a nonlinear and nonlocal Rydberg medium

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