INFINITELY MANY NODAL SOLUTIONS FOR A WEAKLY COUPLED NONLINEAR SCHRÖDINGER SYSTEM

2008 ◽  
Vol 10 (05) ◽  
pp. 651-669 ◽  
Author(s):  
L. A. MAIA ◽  
E. MONTEFUSCO ◽  
B. PELLACCI
Keyword(s):  
Variational Methods ◽  
Nodal Solution ◽  
Radial Solutions ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Nodal Solutions ◽  
Nonlinear Schrödinger ◽  
Nonlinear Schrödinger System ◽  
Weakly Coupled ◽  
Nonlinear Schrodinger Equations ◽  
Schrödinger System

Existence of radial solutions with a prescribed number of nodes is established, via variational methods, for a system of weakly coupled nonlinear Schrödinger equations. The main goal is to obtain a nodal solution with all vector components not identically zero and an estimate on their energies.

scholarly journals Orbital Stability Property for Coupled Nonlinear Schrödinger Equations

2010 ◽  
Vol 10 (3) ◽  
Author(s):  
Liliane de Almeida Maia ◽  
Eugenio Montefusco ◽  
Benedetta Pellacci
Keyword(s):  
Stability Property ◽  
Standing Waves ◽  
Ground States ◽  
Orbital Stability ◽  
Nonlinear Schrödinger Equations ◽  
Schrödinger Equations ◽  
Coupled Nonlinear Schrödinger Equations ◽  
Nonlinear Schrödinger ◽  
Weakly Coupled ◽  
Nonlinear Schrodinger Equations

AbstractOrbital stability property for weakly coupled nonlinear Schrödinger equations is investigated. Different families of orbitally stable standing waves solutions will be found, generated by different classes of solutions of the associated elliptic problem. In particular, orbitally stable standing waves can be generated by least action solutions, but also by solutions with one trivial component whether or not they are ground states. Moreover, standing waves with components propagating with the same frequencies are orbitally stable if generated by vector solutions of a suitable Schrödinger weakly coupled system, even if they are not ground states.

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