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Theory of Multidimensional Solitons
We review a number of topics germane to higher-dimensional solitons in
Bose-Einstein condensates. For dark solitons, we discuss dark band and planar
solitons; ring dark solitons and spherical shell solitons; solitary waves in
restricted geometries; vortex rings and rarefaction pulses; and multi-component
Bose-Einstein condensates. For bright solitons, we discuss instability,
stability, and metastability; bright soliton engineering, including pulsed atom
lasers; solitons in a thermal bath; soliton-soliton interactions; and bright
ring solitons and quantum vortices. A thorough reference list is included.Comment: review paper, to appear as Chapter 5a in "Emergent Nonlinear
Phenomena in Bose-Einstein Condensates: Theory and Experiment," edited by P.
G. Kevrekidis, D. J. Frantzeskakis, and R. Carretero-Gonzalez
(Springer-Verlag