TY - JOUR
T1 - High frequency solutions for the singularly-perturbed one-dimensional nonlinear Schrödinger equation
AU - Felmer, Patricio
AU - Martínez, Salomé
AU - Tanaka, Kazunaga
PY - 2006/10
Y1 - 2006/10
N2 - This article is devoted to the nonlinear Schrödinger equation [InlineMediaObject not available: see fulltext.] when the parameter ε approaches zero. All possible asymptotic behaviors of bounded solutions can be described by means of envelopes, or alternatively by adiabatic profiles. We prove that for every envelope, there exists a family of solutions reaching that asymptotic behavior, in the case of bounded intervals. We use a combination of the Nehari finite dimensional reduction together with degree theory. Our main contribution is to compute the degree of each cluster, which is a key piece of information in order to glue them.
AB - This article is devoted to the nonlinear Schrödinger equation [InlineMediaObject not available: see fulltext.] when the parameter ε approaches zero. All possible asymptotic behaviors of bounded solutions can be described by means of envelopes, or alternatively by adiabatic profiles. We prove that for every envelope, there exists a family of solutions reaching that asymptotic behavior, in the case of bounded intervals. We use a combination of the Nehari finite dimensional reduction together with degree theory. Our main contribution is to compute the degree of each cluster, which is a key piece of information in order to glue them.
UR - http://www.scopus.com/inward/record.url?scp=33747503572&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33747503572&partnerID=8YFLogxK
U2 - 10.1007/s00205-006-0431-8
DO - 10.1007/s00205-006-0431-8
M3 - Article
AN - SCOPUS:33747503572
SN - 0003-9527
VL - 182
SP - 333
EP - 366
JO - Archive for Rational Mechanics and Analysis
JF - Archive for Rational Mechanics and Analysis
IS - 2
ER -