@article{3175393,
    title = "Adiabatic Invariant Approach to Transverse Instability: Landau Dynamics
of Soliton Filaments",
    author = "Kevrekidis, P. G. and Wang, Wenlong and Carretero-Gonzalez, R. and and Frantzeskakis, D. J.",
    journal = "Physical Review and Physical Review Letters Index",
    year = "2017",
    volume = "118",
    number = "24",
    publisher = "AMER PHYSICAL SOC",
    issn = "0094-0003",
    doi = "10.1103/PhysRevLett.118.244101",
    abstract = "Consider 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. 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 or 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."
}