Propagation of wave packets along intensive simple waves

Камчатнов, А. М.; Shaykin, D. V.

doi:10.1063/5.0050618

Cited by 9 publications

(1 citation statement)

References 17 publications

(28 reference statements)

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“…24 An analogous problem involving linear wave-mean field interaction exhibits similar behavior to soliton-mean field interaction, which was studied for the KdV equation in Refs. [36,37]. While (m)KdV, NLS, and KP are all integrable equations, modulation theory can be applied to nonintegrable equations and has been successfully used to analyze solitonmean field interaction in the conduit equation, 2 a model of viscous core-annular fluids, and the Benjamin-Bona-Mahony equation in Ref.…”

Section: Introductionmentioning

confidence: 99%

Soliton–mean field interaction in Korteweg–de Vries dispersive hydrodynamics

Ablowitz

Cole

et al. 2023

Stud Appl Math

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The mathematical description of localized solitons in the presence of large‐scale waves is a fundamental problem in nonlinear science, with applications in fluid dynamics, nonlinear optics, and condensed matter physics. Here, the evolution of a soliton as it interacts with a rarefaction wave or a dispersive shock wave, examples of slowly varying and rapidly oscillating dispersive mean fields, for the Korteweg–de Vries equation is studied. Step boundary conditions give rise to either a rarefaction wave (step up) or a dispersive shock wave (step down). When a soliton interacts with one of these mean fields, it can either transmit through (tunnel) or become embedded (trapped) inside, depending on its initial amplitude and position. A topical review of three separate analytical approaches is undertaken to describe these interactions. First, a basic soliton perturbation theory is introduced that is found to capture the solution dynamics for soliton–rarefaction wave interaction in the small dispersion limit. Next, multiphase Whitham modulation theory and its finite‐gap description are used to describe soliton–rarefaction wave and soliton–dispersive shock wave interactions. Lastly, a spectral description and an exact solution of the initial value problem is obtained through the inverse scattering transform. For transmitted solitons, far‐field asymptotics reveal the soliton phase shift through either type of wave mentioned above. In the trapped case, there is no proper eigenvalue in the spectral description, implying that the evolution does not involve a proper soliton solution. These approaches are consistent, agree with direct numerical simulation, and accurately describe different aspects of solitary wave–mean field interaction.

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Section: Introductionmentioning

confidence: 99%

Soliton–mean field interaction in Korteweg–de Vries dispersive hydrodynamics

Ablowitz

Cole

et al. 2023

Stud Appl Math

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Interactions of certain localized waves for an extended (3+1)-dimensional Kadomtsev-Petviashvili equation in fluid mechanics

Shen,

Tian,

Cheng

et al. 2024

Chinese Journal of Physics

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Description limit for soliton waves due to critical scaling of electrostatic potential

et al. 2021

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We provide a formulation that describes the propagation of solitons in a nondissipative, nonmagnetic plasma, which does not depend on the particular electron density distribution considered. The Poisson equation in the plasma sheath is expressed in terms of the Mach number for ions entering the sheath from the plasma and of a natural scale for the electrostatic potential. We find a class of reference frames with respect to which certain functions become stationary after arbitrary small variations of the Mach number and potential scale, that is, by determining the critical values of those quantities based on a variational method. It is shown that the critical Mach number defines the limits for the applicability of the reductive perturbation technique to a given electron density distribution. Based on our provided potential scale, we show that the Taylor expansion of the suprathermal electron distribution around equilibrium converges for all possible values of the spectral κ-index. In addition, owing to the admissible range for the critical Mach number, it is found that the reductive perturbation technique ceases to be valid for 3/2<κ≤5/2. In the sequel, we show that the technique is not valid for the deformation q-index of nonextensive electrons when q≤3/5. Furthermore, by assuming that the suprathermal and nonextensive solitons are both described with respect to the same critical reference frame, a relation between κ and q, which has been previously obtained on very fundamental grounds, is recovered.

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Propagation of wave packets along intensive simple waves

Cited by 9 publications

References 17 publications

Soliton–mean field interaction in Korteweg–de Vries dispersive hydrodynamics

Soliton–mean field interaction in Korteweg–de Vries dispersive hydrodynamics

Interactions of certain localized waves for an extended (3+1)-dimensional Kadomtsev-Petviashvili equation in fluid mechanics

Description limit for soliton waves due to critical scaling of electrostatic potential

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