scholarly journals Existence and semi-classical limit of the least energy solution to a nonlinear Schrödinger equation with electromagnetic fields

2000 ◽  
Vol 41 (5-6) ◽  
pp. 763-778 ◽  
Author(s):  
Kazuhiro Kurata
Keyword(s):  
Schrödinger Equation ◽  
Electromagnetic Fields ◽  
Nonlinear Schrödinger Equation ◽  
Classical Limit ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Energy Solution ◽  
Nonlinear Schrödinger ◽  
Least Energy Solution ◽  
Least Energy

A symmetry-breaking phenomenon and asymptotic profiles of least-energy solutions to a nonlinear Schrödinger equation

2005 ◽  
Vol 135 (2) ◽  
pp. 357-392 ◽  
Author(s):  
Kazuhiro Kurata ◽  
Tatsuya Watanabe ◽  
Masataka Shibata
Keyword(s):  
Schrödinger Equation ◽  
Symmetry Breaking ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Least Energy Solution ◽  
Image Position ◽  
Least Energy Solutions ◽  
Least Energy

In this paper, we study a symmetry-breaking phenomenon of a least-energy solution to a nonlinear Schrödinger equation under suitable assumptions on V(x), where λ > 1, p > 2 and χA is the characteristic function of the set A = [−(l + 2), −l] ∪ [l,l + 2] with l > 0. We also study asymptotic profiles of least-energy solutions for the singularly perturbed problem for small ε > 0.

SEMI-CLASSICAL LIMIT FOR THE ONE DIMENSIONAL NONLINEAR SCHRÖDINGER EQUATION

2002 ◽  
Vol 04 (03) ◽  
pp. 481-512 ◽  
Author(s):  
PATRICIO L. FELMER ◽  
JUAN J. TORRES
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Classical Limit ◽  
Schrodinger Equation ◽  
Oscillatory Behavior ◽  
Nonlinear Schrodinger Equation ◽  
One Dimensional ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
The One

In this article we study standing wave solutions for the nonlinear Schrödinger equation, which correspond to solutions of the equation [Formula: see text] We are interested in solutions having a prescribed L2 norm, exhibiting high oscillatory behavior and concentrating in an interval. We prove existence of such solutions and we study their asymptotic behavior as the parameter ε goes to zero. In particular we obtain an envelope function describing the amplitude of the solutions and we identify their asymptotic density.

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