TY - JOUR
T1 - On the asymptotic stability of bound states in 2D cubic schrödinger equation
AU - Kirr, E.
AU - Zarnescu, A.
PY - 2007/6
Y1 - 2007/6
N2 - We consider the cubic nonlinear Schrödinger equation in two space dimensions with an attractive potential. We study the asymptotic stability of the nonlinear bound states, i.e. periodic in time localized in space solutions. Our result shows that all solutions with small, localized in space initial data, converge to the set of bound states. Therefore, the center manifold in this problem is a global attractor. The proof hinges on dispersive estimates that we obtain for the non-autonomous, non-Hamiltonian, linearized dynamics around the bound states.
AB - We consider the cubic nonlinear Schrödinger equation in two space dimensions with an attractive potential. We study the asymptotic stability of the nonlinear bound states, i.e. periodic in time localized in space solutions. Our result shows that all solutions with small, localized in space initial data, converge to the set of bound states. Therefore, the center manifold in this problem is a global attractor. The proof hinges on dispersive estimates that we obtain for the non-autonomous, non-Hamiltonian, linearized dynamics around the bound states.
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U2 - 10.1007/s00220-007-0233-3
DO - 10.1007/s00220-007-0233-3
M3 - Article
AN - SCOPUS:34247120263
SN - 0010-3616
VL - 272
SP - 443
EP - 468
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
IS - 2
ER -