Paper Info
Title
Stable Directions for Degenerate Excited States of Nonlinear Schrödinger Equations.
Abstract
We consider nonlinear Schrodinger equations, i partial derivative(t)psi = H-0 psi + lambda vertical bar psi vertical bar(2)psi in R-3 x [0, infinity), where H-0 = -Delta + V, lambda = +/- 1, the potential V is radial and spatially decaying, and the linear Hamiltonian H-0 has only two eigenvalues e(0) < e(1) < 0, where e(0) is simple, and e(1) has multiplicity three. We show that there exist two branches of small "nonlinear excited state" standing-wave solutions, and in both the resonant (e(0) < 2e(1)) and nonresonant (e(0) > 2e(1)) cases, we construct certain finite-codimension regions of the phase space consisting of solutions converging to these excited states at time infinity ("stable directions").
Year
DOI
Venue
2011
10.1137/10079210X
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Keywords
DocType
Volume
symmetry-breaking bifurcation,degenerate eigenvalues,nonlinear excited states,asymptotic dynamics,Schrodinger equations
Journal
43
Issue
ISSN
Citations 
4
0036-1410
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Stephen Gustafson152.79
Tuoc Van Phan210.73