Coupled nonlinear Schrödinger equations with harmonic potential
نویسندگان
چکیده
منابع مشابه
Nonlinear Schrödinger Equations with Repulsive Harmonic Potential and Applications
We study the Cauchy problem for Schrödinger equations with repulsive quadratic potential and power-like nonlinearity. The local problem is well-posed in the same space as that used when a confining harmonic potential is involved. For a defocusing nonlinearity, it is globally well-posed, and a scattering theory is available, with no long range effect for any superlinear nonlinearity. When the no...
متن کامل2 Nonlinear Schrödinger Equations with Repulsive Harmonic Potential and Applications
We study the Cauchy problem for Schrödinger equations with repulsive quadratic potential and power-like nonlinearity. The local problem is well-posed in the same space as that used when a confining harmonic potential is involved. For a defocusing nonlinearity, it is globally well-posed, and a scattering theory is available, with no long range effect for any superlinear nonlinearity. When the no...
متن کاملAnalysis for Nonlinear Schrödinger Equations with Potential
We justify the WKB analysis for the semiclassical nonlinear Schrödinger equation with a subquadratic potential. This concerns subcritical, critical, and supercritical cases as far as the geometrical optics method is concerned. In the supercritical case, this extends a previous result by E. Grenier; we also have to restrict to nonlinearities which are defocusing and cubic at the origin, but besi...
متن کاملThe Nonlinear Schrödinger Equation with a Strongly Anisotropic Harmonic Potential
The nonlinear Schrödinger equation with general nonlinearity of polynomial growth and harmonic confining potential is considered. More precisely, the confining potential is strongly anisotropic; i.e., the trap frequencies in different directions are of different orders of magnitude. The limit as the ratio of trap frequencies tends to zero is carried out. A concentration of mass on the ground st...
متن کاملAsymptotic Stability of Nonlinear Schrödinger Equations with Potential Zhou Gang
We prove asymptotic stability of trapped solitons in the generalized nonlinear Schrödinger equation with a potential in dimension 1 and for even potential and even initial conditions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Arabian Journal of Mathematics
سال: 2017
ISSN: 2193-5343,2193-5351
DOI: 10.1007/s40065-017-0192-2