Stability in turbulence: The interplay between shocks and vorticity in a superfluid with higher-order dispersion

Mossman, Maren; Delikatny, Edward; Forbes, Michael McNeil; Engels, Peter

doi:10.1103/physreva.102.053310

Cited by 5 publications

(3 citation statements)

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“…where 𝑡 ≥ 𝑇 1 > 0. Next, the soliton position while on the linear ramp is computed from (20). Again, using the soliton ansatz over the linear portion of the RW gives…”

Section: Soliton-rarefaction Wave Dynamicsmentioning

confidence: 99%

“…Superfluids are another medium in which nonlinearity due to particle interactions and dispersion resulting from quantum matter wave interference lead to solitons and DSWs. [17][18][19][20] Solitons and DSWs have also been studied in stressed solids and magnetic materials. [21][22][23] The motivation for this focused review is the rapid and varied mathematical developments on this problem that have occurred within only a few years.…”

Section: Introductionmentioning

confidence: 99%

“…There has been significant interest in the propagation of large‐scale mean fields in spatial and fiber nonlinear optics, 13–16 where fundamental DSW properties have been favorably compared with Whitham modulation theory. Superfluids are another medium in which nonlinearity due to particle interactions and dispersion resulting from quantum matter wave interference lead to solitons and DSWs 17–20 . Solitons and DSWs have also been studied in stressed solids and magnetic materials 21–23 …”

Section: Introductionmentioning

confidence: 99%

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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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“…where 𝑡 ≥ 𝑇 1 > 0. Next, the soliton position while on the linear ramp is computed from (20). Again, using the soliton ansatz over the linear portion of the RW gives…”

Section: Soliton-rarefaction Wave Dynamicsmentioning

confidence: 99%