Solitons and nonlinear waves along quantum vortex filaments under the low-temperature two-dimensional local induction approximation

Gorder, Robert A. Van

doi:10.1103/physreve.93.052208

Cited by 8 publications

(7 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One may compare this result with the t 1/2 similarity scaling obtained for the 2D-LIA directly 17 or for the transformed solutions governed by the first equation in the WKIS hierarchy. 18 The t 1/2 type scalings also appear in numerical studies for the LIA or Biot-Savart model, in addition to the fully non-local Biot-Savart asymptotics which were recently studied in Ref. 57; see, for instance, Eqs.…”

Section: Self-similar Vortex Filament Structuresmentioning

confidence: 94%

“…Related stationary solutions were also obtained for the Wadati-Konno-Ichikawa-Shimizu (WKIS) equations and then mapped into the 2D-LIA in Ref. 18. The unifying theme behind all of these stationary solutions is that they can be used to model filaments which maintain their geometric form while rotating and translating in space.…”

Section: B General Filaments Moving Without Change Of Formmentioning

confidence: 99%

See 1 more Smart Citation

Motion of isolated open vortex filaments evolving under the truncated local induction approximation

Gorder

2017

Physics of Fluids

Self Cite

View full text Add to dashboard Cite

The study of nonlinear waves along open vortex filaments continues to be an area of active research. While the local induction approximation (LIA) is attractive due to locality compared with the nonlocal Biot-Savart formulation, it has been argued that LIA appears too simple to model some relevant features of Kelvin wave dynamics, such as Kelvin wave energy transfer. Such transfer of energy is not feasible under the LIA due to integrability, so in order to obtain a non-integrable model, a truncated LIA, which breaks the integrability of the classical LIA, has been proposed as a candidate model with which to study such dynamics. Recently Laurie et al. ["Interaction of Kelvin waves and nonlocality of energy transfer in superfluids," Phys. Rev. B 81, 104526 (2010)] derived truncated LIA systematically from Biot-Savart dynamics. The focus of the present paper is to study the dynamics of a section of common open vortex filaments under the truncated LIA dynamics. We obtain the analog of helical, planar, and more general filaments which rotate without a change in form in the classical LIA, demonstrating that while quantitative differences do exist, qualitatively such solutions still exist under the truncated LIA. Conversely, solitons and breather solutions found under the LIA should not be expected under the truncated LIA, as the existence of such solutions relies on the existence of an infinite number of conservation laws which is violated due to loss of integrability. On the other hand, similarity solutions under the truncated LIA can be quite different to their counterparts found for the classical LIA, as they must obey a t 1/3 type scaling rather than the t 1/2 type scaling commonly found in the LIA and Biot-Savart dynamics. This change in similarity scaling means that Kelvin waves are radiated at a slower rate from vortex kinks formed after reconnection events. The loss of soliton solutions and the difference in similarity scaling indicate that dynamics emergent under the truncated LIA can indeed differ a great deal from those previously studied under the classical LIA.

show abstract

Section: Self-similar Vortex Filament Structuresmentioning

confidence: 94%

Section: B General Filaments Moving Without Change Of Formmentioning

confidence: 99%

Motion of isolated open vortex filaments evolving under the truncated local induction approximation

Gorder

2017

Physics of Fluids

Self Cite

View full text Add to dashboard Cite

show abstract

“…In the case of ideal inviscid fluid, the motion of the fluid elements is constrained by Biot-Savart law, which provides valuable information about vortex tangles [5,6]. In particular, a variety of excitations are generated and evolve along the vortex filament due to the self-induced velocity [7][8][9][10][11]. Such excitations are physically important since they turn out to be the main degrees of freedom remaining in a superfluid in the ultra low temperature regime.…”

Section: Introductionmentioning

confidence: 99%

Breather-induced quantised superfluid vortex filaments and their characterisation

Liu

Zhao

et al. 2020

Commun. Theor. Phys.

View full text Add to dashboard Cite

We study and characterise the breather-induced quantised superfluid vortex filaments which correspond to the Kuznetsov-Ma breather and super-regular breather excitations developing from localised perturbations. Such vortex filaments, emerging from an otherwise perturbed helical vortex, exhibit intriguing loop structures corresponding to the large amplitude of breathers due to the dual action of bending and twisting of the vortex. The loop induced by the Kuznetsov-Ma breather emerges periodically as time increases, while the loop structure triggered by the super-regular breather—the loop pair—exhibits striking symmetry breaking due to the broken reflection symmetry of the group velocities of the super-regular breather. In particular, we identify explicitly the generation conditions of these loop excitations by introducing a physical quantity—the integral of the relative quadratic curvature—which corresponds to the effective energy of breathers. Despite the nature of nonlinearity, it is demonstrated that this physical quantity shows a linear correlation with the loop size. These results will deepen our understanding of breather-induced vortex filaments and be helpful for controllable ring-like excitations on the vortices.

show abstract

“…In the case of ideal inviscid fluid, the motion of the fluid elements is constrained by Biot-Savart law which provides valuable information of vortex tangles [5,6]. In particular, a variety of excitations are generated and evolve along the vortex filament due to the self-induced velocity [7][8][9][10][11]. Such excitations are physically important since they turn out to be the main degrees of freedom remaining in a superfluid in the ultra low temperature regime.…”

Section: Introductionmentioning

confidence: 99%

Breather induced quantized superfluid vortex filaments and their characterization

Li,

Liu,

Zhao

et al. 2019

Preprint

View full text Add to dashboard Cite

We study and characterize the breather-induced quantized superfluid vortex filaments which correspond to the Kuznetsov-Ma breather and super-regular breather excitations developing from localised perturbations. Such vortex filaments, emerging from an otherwise perturbed helical vortex, exhibit intriguing loop structures corresponding to the large amplitude of breathers due to the dual action of bending and twisting of the vortex. The loop induced by Kuznetsov-Ma breather emerges periodically as time increases, while the loop structure triggered by super-regular breather-the loop pair -exhibits striking symmetry breaking due to the broken reflection symmetry of the group velocities of super-regular breather. In particular, we identify explicitly the generation conditions of these loop excitations by introducing a physical quantity-the integral of the relative quadratic curvature-which corresponds to the effective energy of breathers. Although the nature of nonlinearity, it is demonstrated that this physical quantity shows a linear correlation with the loop size. These results will deepen our understanding of breather-induced vortex filaments and be helpful for controllable ring-like excitations on the vortices.

show abstract

Solitons and nonlinear waves along quantum vortex filaments under the low-temperature two-dimensional local induction approximation

Cited by 8 publications

References 53 publications

Motion of isolated open vortex filaments evolving under the truncated local induction approximation

Motion of isolated open vortex filaments evolving under the truncated local induction approximation

Breather-induced quantised superfluid vortex filaments and their characterisation

Breather induced quantized superfluid vortex filaments and their characterization

Contact Info

Product

Resources

About