Semiclassical Standing Waves with Clustering Peaks for Nonlinear Schrödinger Equations / Jaeyoung Byeon, Kazunaga Tanaka.

Format:

Book

Author/Creator:

Byeon, Jaeyoung, 1966- author.

Tanaka, Kazunaga, 1959- author.

Series:

Memoirs of the American Mathematical Society ; no. 1076.

Memoirs of the American Mathematical Society, 0065-9266 ; number 1076

Language:

English

Subjects (All):

Gross-Pitaevskii equations.

Schrödinger equation.

Standing waves.

Cluster analysis.

Physical Description:

vii, 89 pages ; 26 cm.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2014.

Language Note:

Text in English.

Contents:

Preliminaries

Notation

Limit problems

Estimate of with relation to the Pohozaev identity

Functional setting

Choice of a neighborhood O of M

Control on small parts of

Local centers of mass

Some functions in terms of local centers of mass

Neighborhood and minimization for a tail of u in

A choice of parameters and minimization

Invariant new neighborhoods

Width of a set

A gradient estimate for the energy functional

E-dependent concentration-compactness argument

A gradient estimate

Gradient flow of the energy functional

Translation flow associated to a gradient flow of V (x) on R

A pseudo-gradient flow on associated V

Definition of a translation operator

Properties of the translation operator

Iteration procedure for the gradient flow and the translation flow

An (N + l) - dimensional initial path and an intersection result

A preliminary path

An initial path

An intersection property

Completion of the proof of Theorem 1.3

Proof of Proposition 8.3

An interaction estimate

Preliminary asymptotic estimates

Proof of Proposition 10.1

Proof of Lemma 6.1

Generalization to a saddle point setting

Saddle point setting

Proof of Theorem 12.1.

Notes:

"May 2014, volume 229, number 1076 (third of 5 numbers)."

Includes bibliographical references.

ISBN:

9780821891636

0821891634

OCLC:

867024631