Orbital stability of bound states of nonlinear Schrödinger equations with linear and nonlinear lattices
نویسندگان
چکیده
We study the orbital stability and instability of single-spike bound states of critical semi-classical nonlinear Schrödinger equations (NLS) with linear and nonlinear lattices. These equations may model an inhomogeneous Bose-Einstein condensate and an optical beam in a nonlinear lattice. When the linear lattice is 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 the linear lattice is turned on, we consider three different cases and obtain the most general theorem on the orbital stability problem for NLS with linear and nonlinear lattices.
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