The Semiclassical Limit of the Nonlinear Schrödinger Equation in a Radial Potential
- 作者：Benci ; Vieri ; D'Aprile ; Teresa
- 刊名：Journal of Differential Equations
- 出版年：2002
- 期刊代码：74_00220396
- 类别：mt
- 出版时间：September 1, 2002
- 卷：184
- 期：1
- 页码：109-138
- 文件大小：289 K
摘要
In this paper, we are concerned with the following nonlinear Schrödinger equation: ih=−Δψ+V(x)ψ−γh
ψp−2ψ, γh>0, x
R2, where h>0, 2<p<6, ψ : R2→C, and the potential V is radially symmetric. Our main purpose is to obtain positive solutions among the functions having the form ψ(r,θ,t)=exp(Imhθ/h+iEt/h)v(r), being r,θ the polar coordinates in the plane. Since we assume Mh>0, the functions in this special class have nontrivial angular momentum as it will be specified in the Introduction. Furthermore, our solutions exhibit a “spike-layer” pattern when the parameter h approaches zero; our object is to analyse the appearance of such type of concentration asymptotic behaviour in order to locate the asymptotic peaks.
ψp−2ψ, γh>0, xR2, where h>0, 2<p<6, ψ : R2→C, and the potential V is radially symmetric. Our main purpose is to obtain positive solutions among the functions having the form ψ(r,θ,t)=exp(Imhθ/h+iEt/h)v(r), being r,θ the polar coordinates in the plane. Since we assume Mh>0, the functions in this special class have nontrivial angular momentum as it will be specified in the Introduction. Furthermore, our solutions exhibit a “spike-layer” pattern when the parameter h approaches zero; our object is to analyse the appearance of such type of concentration asymptotic behaviour in order to locate the asymptotic peaks.