Multi-bump bound states of nonlinear Schrödinger equations with electromagnetic fields and critical frequency
type: Item
instance of: scholarly article
title: Multi-bump bound states of nonlinear Schrödinger equations with electromagnetic fields and critical frequency
zbMATH Open document ID: 1180.35237
author: Zhongwei Tang
published in: Journal of Differential Equations
publication date: 2008-11-12T00:00:00Z
review text: The author deals with nonlinear Schrödinger equations with an electromagnetic potential \[ i\frac{\partial\psi}{\partial t}=-(\nabla+i A(x))^2 \psi+\lambda W(x)\psi-f(|\psi|^2)\psi,\;(t,x)\in\mathbb{R} \times\mathbb{R}^N,\tag{1} \] where \(i\) is the imaginary unit, \(\lambda\) is the parameter corresponding to Plank constant, \(A(x)=(A_1(x),\dots,A_N (x))\) is a real vector (magnetic) potential and \(W(x)\) is a scalar electric potential. The author is interested in standing wave solutions, that is \[ \psi(t,x)=\exp(-i\lambda Et)u(t)\tag{2} \] to (1) when \(\lambda\) is sufficiently large, where \(E\) is a real number and \(u(x)\) is a complex-valued function which satisfies \[ -(\nabla+iA(x))^2u(x)+\lambda (W(x)-E)u(x)=f\left(| u(x)|^2\right)u(x),\;x\in\mathbb{R}^N.\tag{3} \] In the present study the author considers the existence of multi-bump solutions to (3).
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J60
Mathematics Subject Classification ID: 35B33
zbMATH DE Number: 5365149
zbMATH Keywords: nonlinear Schrödinger equation
zbMATH Keywords: multi-bump standing waves
zbMATH Keywords: potential well
zbMATH Keywords: magnetic fields
zbMATH Keywords: variational methods
MaRDI profile type: Publication
full work available at URL: j.jde.2008.07.035
OpenAlex ID: W2001297055
cites work: Semiclassical states of nonlinear Schrödinger equations
cites work: Multiplicity results for some nonlinear Schrödinger equations with potentials
cites work: A semilinear Schrödinger equation in the presence of a magnetic field
cites work: On multi-bump semi-classical bound states of nonlinear Schrödinger equations with electromagnetic fields
cites work: Standing waves with a critical frequency for nonlinear Schrödinger equations
cites work: Standing waves with a critical frequency for nonlinear Schrödinger equations. II.
cites work: Multi-bump standing waves with a critical frequency for nonlinear Schrödinger equations
cites work: Existence and uniqueness of multi-bump bound states of nonlinear Schrödinger equations with electromagnetic fields
cites work: Semiclassical stationary states of nonlinear Schrödinger equations with an external magnetic field.
cites work: Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions
cites work: Multiple positive solutions to nonlinear Schrödinger equations with competing potential functions
cites work: Semiclassical limit for nonlinear Schrödinger equations with electromagnetic fields
cites work: Semiclassical states for NLS equations with magnetic potentials having polynomial growths
cites work: Multi-peak periodic semiclassical states for a class of nonlinear Schrödinger equations
cites work: Multi-peak bound states for nonlinear Schrödinger equations
cites work: Semi-classical states for nonlinear Schrödinger equations
cites work: Multiplicity of positive solutions of a nonlinear Schrödinger equation
cites work: Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential
cites work: Q5187597
cites work: Existence and semi-classical limit of the least energy solution to a nonlinear Schrödinger equation with electromagnetic fields
cites work: On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential
cites work: Existence of Semiclassical Bound States of Nonlinear Schrödinger Equations with Potentials of the Class (V)a
cites work: On the least energy solutions of nonlinear Schrödinger equations with electromagnetic fields
cites work: Multiplicity of standing wave solutions of nonlinear Schrödinger equations with electromagnetic fields
DOI: 10.1016/J.JDE.2008.07.035
description: scientific article; zbMATH DE number 5365149