Stable two-dimensional soliton and vortex structures at the upper-hybrid resonance

V. M. Lashkin
Institute for Nuclear Research, Pr. Nauki 47, Kiev 03680, Ukraine
Abstract. Two-dimensional (2D) equations describing the nonlinear interaction between upper-hybrid and dispersive magnetosonic
waves are presented. Nonlocal nonlinearity in the equations results in the possibility of existence of stable 2D
nonlinear structures. A rigorous proof of the absence of collapse in the model is given. 2D soliton, vortex and multisoliton
solutions are found numerically. It is shown that 2D solitons with negative hamiltonian are stable and do not collapse.
Keywords: upper-hybrid resonance, soliton, multisoliton, vortex, collapse
Upper-hybrid (UH) waves are frequently observed in space plasma, both in the ionosphere and in the magnetosphere.
One-dimensional (1D) theory of the nonlinear upper-hybrid waves interacting with the low-frequency motions of
magnetosonic type was developed in [1, 2, 3, 4, 5, 6], where, in particular, 1D nonlinear soliton structures were found
both numerically and analytically. Here, we present 2D analysis and find numerically soliton, multisoliton (dipole, twohump
and quadrupole), and vortex ring-like structures. We show that the nonlinear 2D structures at the upper-hybrid
resonance can be stable. Dispersion of the magnetosonic wave effectively introduces a nonlocal nonlinear interaction
and we present the rigorous proof of the absence of collapse.
In the linear approximation, the UH waves are characterized by the dispersion relation

is the Fourier transform of the linear operator in the left-hand side of Eq. (2) evaluated at k0
 k, and d =

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