Multiple branches of travelling waves for the Gross–Pitaevskii equation

Chiron, David; Scheid, Claire

doi:10.1088/1361-6544/aab4cc

Cited by 19 publications

(46 citation statements)

References 40 publications

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“…We refer to Theorem 44 in Section 5 for a more precisely statement of this result. We note that the Morse index of the lump solution is numerically shown to be one ( [15]). Here we give a rigorous proof.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 92%

Nondegeneracy, Morse Index and Orbital Stability of the KP-I Lump Solution

Liu

Wei

2019

Arch Rational Mech Anal

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Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 92%

Nondegeneracy, Morse Index and Orbital Stability of the KP-I Lump Solution

Liu

Wei

2019

Arch Rational Mech Anal

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“…Such a structure, is sometimes referred to as vortexonium [117], and it is hard to discern individual vortex phases although it remains a spatially localized bound state. More appropriately, this structure is known as the Jones-Roberts (JR) soliton (see, e.g., the recent discussion in [118]) and it has been recently considered also experimentally [119]. As can be seen in Fig.…”

Section: Density Evolutionmentioning

confidence: 99%

Quench induced vortex-bright-soliton formation in binary Bose-Einstein condensates

Mukherjee

Mistakidis

Kevrekidis

et al. 2020

J. Phys. B: At. Mol. Opt. Phys.

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We unravel the spontaneous generation of vortex-bright-soliton structures in binary Bose-Einstein condensates with a small mass imbalance between the species confined in a two-dimensional harmonic trap where one of the two species has been segmented into two parts by a potential barrier. To trigger the dynamics the potential barrier is suddenly removed and subsequently the segments perform a counterflow dynamics. We consider a relative phase difference of π between the segments, while a singly quantized vortex may be imprinted at the center of the other species. The number of vortex structures developed within the segmented species following the merging of its segments is found to depend on the presence of an initial vortex on the other species. In particular, a π phase difference in the segmented species and a vortex in the other species result in a single vortex-bright-soliton structure. However, when the non-segmented species does not contain a vortex the counterflow dynamics of the segmented species gives rise to a vortex dipole in it accompanied by two bright solitary waves arising in the non-segmented species. Turning to strongly mass imbalanced mixtures, with a heavier segmented species, we find that the same overall dynamics takes place, while the quench-induced nonlinear excitations become more robust. Inspecting the dynamics of the angular momentum we show that it can be transferred from one species to the other, and its transfer rate can be tuned by the strength of the interspecies interactions and the mass of the atomic species.

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“…Indeed, an example of such periodic solutions, returning to themselves upon running around the torus are traveling solutions, such as the lump ones spontaneously encountered herein. Given their potential connection to so-called KP-lumps [43], this is an interesting direction in its own right. Indeed, given the success of the particle model herein, exploring additional directions such as the potential ordered and chaotic orbits [44] at the low-dimensional dynamical systems level could also hold some appeal.…”

Section: Discussionmentioning

confidence: 99%

Superfluid vortex multipoles and soliton stripes on a torus

D'Ambroise,

Carretero-González,

Schmelcher

et al. 2022

Preprint

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We study the existence, stability, and dynamics of vortex dipole and quadrupole configurations in the nonlinear Schrödinger (NLS) equation on the surface of a torus. For this purpose we use, in addition to the full two-dimensional NLS on the torus, a recently derived [Phys. Rev. A 101, 053606 (2021)] reduced point-vortex particle model which is shown to be in excellent agreement with the full NLS evolution. Horizontal, vertical, and diagonal stationary vortex dipoles are identified and continued along the torus aspect ratio and the chemical potential of the solution. Windows of stability for these solutions are identified. We also investigate stationary vortex quadrupole configurations. After eliminating similar solutions induced by invariances and symmetries, we find a total of 16 distinct configurations ranging from horizontal and vertical aligned quadrupoles, to rectangular and rhomboidal quadrupoles, to trapezoidal and irregular quadrupoles. The stability for the least unstable and, potentially, stable quadrapole solutions is monitored both at the NLS and the reduced model levels. Two quadrupole configurations are found to be stable on small windows of the torus aspect ratio and a handful of quadrupoles are found to be very weakly unstable for relatively large parameter windows. Finally, we briefly study the dark soliton stripes and their connection, through a series of bifurcation cascades, with steady state vortex configurations.

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Multiple branches of travelling waves for the Gross–Pitaevskii equation

Cited by 19 publications

References 40 publications

Nondegeneracy, Morse Index and Orbital Stability of the KP-I Lump Solution

Nondegeneracy, Morse Index and Orbital Stability of the KP-I Lump Solution

Quench induced vortex-bright-soliton formation in binary Bose-Einstein condensates

Superfluid vortex multipoles and soliton stripes on a torus

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