Orbital stability of bound states of nonlinear Schrodinger equations with linear and nonlinear optical lattices

Details Orbital stability of bound states of nonlinear Schrodinger equations with linear and nonlinear optical lattices Orbital stability of bound states of nonlinear Schrodinger equations with linear and nonlinear optical lattices

2010-06-24

arxiv.org/abs/1006.4671v1

Mathematics

Analysis of PDEs

to appear in Journal of Differential Equations

Scientific paper

We study the orbital stability and instability of single-spike bound states of semiclassical nonlinear Schrodinger (NLS) equations with critical exponent, linear and nonlinear optical lattices (OLs). These equations may model two-dimensional Bose-Einstein condensates in linear and nonlinear OLs. When linear OLs are switched off, we derive the asymptotic expansion formulas and obtain necessary conditions for the orbital stability and instability of single-spike bound states, respectively. When linear OLs are turned on, we consider three different conditions of linear and nonlinear OLs to develop mathematical theorems which are most general on the orbital stability problem.

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