03399nam 2200625 450 991078719680332120180613002136.01-4704-1530-5(CKB)3710000000230213(EBL)3114200(SSID)ssj0001108988(PQKBManifestationID)11643290(PQKBTitleCode)TC0001108988(PQKBWorkID)11109855(PQKB)11629100(MiAaPQ)EBC3114200(RPAM)17985420(PPN)195408616(EXLCZ)99371000000023021320150417h20132013 uy 0engur|n|---|||||txtccrSemiclassical standing waves with clustering peaks for nonlinear Schrödinger equations /Jaeyoung Byeon, Kazunaga TanakaProvidence, Rhode Island :American Mathematical Society,2013.©20131 online resource (104 p.)Memoirs of the American Mathematical Society,1947-6221 ;Volume 229, Number 1076"Volume 229, Number 1076 (third of 5 numbers)."0-8218-9163-4 Includes bibliographical references.""4.1. A choice of parameters and minimization""""4.2. Invariant new neighborhoods""; ""4.3. Width of a set Ì? ( â€?, â€?)â??Ì? ( â€?, â€?)""; ""Chapter 5. A gradient estimate for the energy functional""; ""5.1. -dependent concentration-compactness argument""; ""5.2. A gradient estimate""; ""5.3. Gradient flow of the energy functional Î?_{ }""; ""Chapter 6. Translation flow associated to a gradient flow of ( ) on \R^{ }""; ""6.1. A pseudo-gradient flow on \overline{ }_{3 â?€}( )^{â??â?€} associated to ( â??)+\cdots+ ( _{â??â?€})""""6.2. Definition of a translation operator""""6.3. Properties of the translation operator""; ""Chapter 7. Iteration procedure for the gradient flow and the translation flow""; ""Chapter 8. An ( +1)â??â?€-dimensional initial path and an intersection result""; ""8.1. A preliminary path â?€""; ""8.2. An initial path _{1 }""; ""8.3. An intersection property""; ""Chapter 9. Completion of the proof of Theorem 1.3""; ""Chapter 10. Proof of Proposition 8.3""; ""10.1. An interaction estimate""; ""10.2. Preliminary asymptotic estimates""; ""10.3. Proof of Proposition 10.1""""Chapter 11. Proof of Lemma 6.1""""Chapter 12. Generalization to a saddle point setting""; ""12.1. Saddle point setting""; ""12.2. Proof of Theorem 12.1""; ""Acknowledgments""; ""Bibliography""Memoirs of the American Mathematical Society ;Volume 229, Number 1076.Gross-Pitaevskii equationsSchrödinger equationStanding wavesCluster analysisGross-Pitaevskii equations.Schrödinger equation.Standing waves.Cluster analysis.530.12/4Byeon Jaeyoung1966-1583595Tanaka Kazunaga1959-MiAaPQMiAaPQMiAaPQBOOK9910787196803321Semiclassical standing waves with clustering peaks for nonlinear Schrödinger equations3866877UNINA