Stabilization of two-dimensional solitons and vortices againstsupercritical collapse by lattice potentials
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- 作者：R. Driben and B. A. Malomed
- 关键词：PACS 03.75.Lm Tunneling ; Josephson effect ; Bose ; Einstein condensates in periodic potentials ; solitons ; vortices ; and topological excitations ; 05.45.Yv Solitons ; 42.65.Tg Optical solitons ; nonlinear guided waves ; 42.70.Nq Other nonlinear optical materia
- 刊名：The European Physical Journal D - Atomic ; Molecular and Optical Physics
- 出版时间：December, 2008
- 出版年：2008
- 期刊代码：37_1434-6060
- 类别：bus
- 卷：50
- 期：3
- 页码：317-323
- 数据来源：sp
摘要
It is known that optical-lattice (OL) potentials can stabilize solitons and solitary vortices against the critical collapse, generated by cubic attractive nonlinearity in the 2D geometry. We demonstrate that OLs can also stabilize various species of fundamental and vortical solitons against the supercritical collapse, driven by the double-attractive cubic-quintic nonlinearity (however, solitons remain unstable in the case of the pure quintic nonlinearity). Two types of OLs are considered, producing similar results: the 2D Kronig-Penney “checkerboard”, and the sinusoidal potential. Soliton families are obtained by means of a variational approximation, and as numerical solutions. The stability of all families, which include fundamental and multi-humped solitons, vortices of oblique and straight types, vortices built of quadrupoles, and supervortices, strictly obeys the Vakhitov-Kolokolov criterion. The model applies to optical media and BEC in “pancake” traps.