Instability of Standing Waves to the Inhomogeneous Nonlinear Schrödinger Equation with Harmonic Potential
نویسندگان
چکیده
We study the instability of standing-wave solutions eφω(x) to the inhomogeneous nonlinear Schrödinger equation iφt = −4φ + |x|2φ− |x|b|φ|p−1φ, x ∈ R , where b > 0 and φω is a ground-state solution. The results of the instability of standing-wave solutions reveal a balance between the frequency ω of wave and the power of nonlinearity p for any fixed b > 0.
منابع مشابه
Instability of Standing Waves of the Schrödinger Equation with Inhomogeneous Nonlinearity
This paper is concerned with the inhomogeneous nonlinear Shrödinger equation (INLS-equation) iut +∆u+ V ( x)|u|u = 0, x ∈ R . In the critical and supercritical cases p ≥ 4/N, with N ≥ 2, it is shown here that standing-wave solutions of (INLS-equation) on H1(RN ) perturbation are nonlinearly unstable or unstable by blow-up under certain conditions on the potential term V with a small > 0.
متن کاملSharp global existence condition and instability by blowup for an inhomogeneous L critical nonlinear Schrödinger equation
An inhomogeneous nonlinear Schrödinger equation is considered, which is invariant under L scaling. The sharp condition for global existence of H solutions is established, involving the L norm of the ground state of the stationary equation. Strong instability of standing waves is proved by constructing self-similar solutions blowing up in finite time.
متن کاملLocalized standing waves in inhomogeneous Schrödinger equations
A nonlinear Schrödinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a combination of self-focusing and self-defocusing nonlinearity, with the self-defocusing region localized in a finite interval, is investigated. Using numerical computa...
متن کاملStability of Standing Waves for Nonlinear Schrödinger Equations with Inhomogeneous Nonlinearities
The effect of inhomogeneity of nonlinear medium is discussed concerning the stability of standing waves eφω(x) for a nonlinear Schrödinger equation with an inhomogeneous nonlinearity V (x)|u|p−1u, where V (x) is proportional to the electron density. Here, ω > 0 and φω(x) is a ground state of the stationary problem. When V (x) behaves like |x|−b at infinity, where 0 < b < 2, we show that eφω(x) ...
متن کاملInstability of bound states of a nonlinear Schrödinger equation with a Dirac potential
We study analytically and numerically the stability of the standing waves for a nonlinear Schrödinger equation with a point defect and a power type nonlinearity. A main difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves, and it is overcome by a perturbation method and continuation arguments. Among others, in the case of a repulsive d...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008