An Adiabatic Invariant Approach to Transverse Instability: Landau Dynamics of Soliton Filaments

Abstract

Assume a lower-dimensional solitonic structure embedded in a higher dimensional space, e.g., a 1D dark soliton embedded in 2D space, a ring dark soliton in 2D space, a spherical shell soliton in 3D space etc. By extending the Landau dynamics approach [Phys. Rev. Lett. {\bf 93}, 240403 (2004)], we show that it is possible to capture the transverse dynamical modes (the "Kelvin modes") of the undulation of this "soliton filament" within the higher dimensional space. These are the transverse stability/instability modes and are the ones potentially responsible for the breakup of the soliton into structures such as vortices, vortex rings etc. We present the theory and case examples in 2D and 3D, corroborating the results by numerical stability and dynamical computations.

5 pages, 3 figures

References in corpus (5)

• Controlling the transverse instability of dark solitons and nucleation of vortices by a potential barrier
• Dark solitons as quasiparticles in trapped condensates
• Bending-wave Instability of a Vortex Ring in a Trapped Bose-Einstein Condensate
• Parametric Auto-Excitation of Magnetic Droplet Soliton Perimeter Modes
• Dynamics of ring dark solitons in Bose-Einstein condensates and nonlinear optics

Cited by in corpus (20)

• The impact of ultra-light axion self-interactions on the large scale structure of the Universe
• Parametrically excited star-shaped patterns at the interface of binary Bose-Einstein condensates
• Spontaneous Formation of Star-Shaped Surface Patterns in a Driven Bose-Einstein Condensate
• Reduced dynamics for one and two dark soliton stripes in the defocusing nonlinear Schrödinger equation: a variational approach
• Many-Body Quantum Dynamics in the Decay of Bent Dark Solitons of Bose-Einstein Condensates
• Solitary waves in a quantum droplet-bearing system
• Spectral and dynamical analysis of a single vortex ring in anisotropic harmonically trapped three-dimensional Bose-Einstein condensates
• A direct derivation of the dark soliton excitation energy
• Dark-bright solitons in spinor polariton condensates under nonresonant pumping
• Hydrodynamics and two-dimensional dark lump solitons for polariton superfluids
• Planar and Radial Kinks in Nonlinear Klein-Gordon Models: Existence, Stability and Dynamics
• Controlled engineering of a vortex-bright soliton dynamics using a constant driving force
• Pairwise Interactions of Ring Dark Solitons with Vortices and other Rings: Stationary States, Stability Features and Nonlinear Dynamics
• Dynamics of interacting dark soliton stripes
• Adiabatic invariant analysis of dark and dark-bright soliton stripes in two-dimensional Bose-Einstein condensates
• Dynamics and stabilization of bright soliton stripes in the hyperbolic-dispersion nonlinear Schrödinger equation
• Bogoliubov-de Gennes theory of the "snake" instability of gray solitons in higher dimensions
• Transverse instabilities of stripe domains in magnetic thin films with perpendicular magnetic anisotropy
• Nonlinear Waves in an Experimentally Motivated Ring-shaped Bose-Einstein Condensate Setup
• Variational Approach to the Snake Instability of a Bose-Einstein Condensate Soliton