Stability of Exact Solutions of the Defocusing Nonlinear Schrr Odinger Equation with Periodic Potential in Two Dimensions
نویسندگان
چکیده
The cubic nonlinear Schrr odinger equation with repulsive nonlinearity and elliptic function potential in two-dimensions models a repulsive dilute gas Bose{Einstein condensate in a lattice potential. A family of exact stationary solutions is presented and its stability is examined using analytical and numerical methods. All stable trivial-phase solutions are oo-set from the zero level. Our results imply that a large number of condensed atoms is suucient to form a stable, periodic condensate.
منابع مشابه
Defocusing Nonlinear Schrr Odinger Equation: Connnement, Stability and Asymptotic Stability Keywords. Nonlinear Schrr Odinger Equation { Dispersion {pseudo-con- Formal Law { Time-dependent Rescalings { Stability { Large Time Asymp- Totics { Minimzers { Relative Entropy { Csiszz Ar-kullback Inequality
This paper is devoted to the asymptotic properties of the Nonlinear Schrr odinger equation in the defocusing case. We recover dispersion rates by the mean of time-dependent rescalings in the power law case and prove a new result in the case of the logarithmic Nonlinear Schrr odinger equation. The rescaled equation is then used to obtain an asymptotic result of nonlinear stability, which is the ...
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