NONLINEAR DIRAC EQUATION ON GRAPHS WITH LOCALIZED NONLINEARITIES: BOUND STATES AND NONRELATIVISTIC LIMIT

被引：24

作者：

Borrelli, William ^{[1
]}

Carlone, Raffaele ^{[2
]}

Tentarelli, Lorenzo ^{[2
]}

机构：

[1] Univ Paris 09, PSL Res Univ, CNRS, UMR 7534, F-75016 Paris, France

[2] Univ Federico II Napoli, Dipartimento Matemat & Applicaz R Caccioppoli, MSA, Via Cinthia, I-80126 Naples, Italy

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2019年 / 51卷 / 02期

关键词：

nonlinear Dirac equations; metric graphs; nonrelativistic limit; variational methods; bound states; linking; GROUND-STATES; NLS EQUATION; SCHRODINGER-EQUATION; STATIONARY SOLUTIONS; STANDING WAVES; QUANTUM GRAPHS; METRIC GRAPHS; STABILITY; COMPACT; OPERATOR;

D O I：

10.1137/18M1211714

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the nonlinear Dirac (NLD) equation on noncompact metric graphs with localized Kerr nonlinearities, in the case of Kirchhoff-type conditions at the vertices. Precisely, we discuss existence and multiplicity of the bound states (arising as critical points of the NLD action functional) and we prove that, in the L-2-subcritical case, they converge to the bound states of the nonlinear Schrodinger equation in the nonrelativistic limit.

引用

页码：1046 / 1081

页数：36

共 50 条

[31] Weakly localized states for nonlinear Dirac equations
William Borrelli
Calculus of Variations and Partial Differential Equations, 2018, 57
[32] Weakly localized states for nonlinear Dirac equations
Borrelli, William
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2018, 57 (06)
[33] Dynamics of the nonlinear Klein-Gordon equation in the nonrelativistic limit
Pasquali, S.
ANNALI DI MATEMATICA PURA ED APPLICATA, 2019, 198 (03) : 903 - 972
[34] UNIFORMLY ACCURATE NESTED PICARD ITERATIVE INTEGRATORS FOR THE DIRAC EQUATION IN THE NONRELATIVISTIC LIMIT REGIME
Cai, Yongyong
Wang, Yan
SIAM JOURNAL ON NUMERICAL ANALYSIS, 2019, 57 (04) : 1602 - 1624
[35] Elementary doublets of bound states of the radial Dirac equation
Znojil, M
MODERN PHYSICS LETTERS A, 1999, 14 (13) : 863 - 868
[36] On the bound states of the Dirac equation in the extreme Kerr metric
Batic, D.
Nowakowski, M.
CLASSICAL AND QUANTUM GRAVITY, 2008, 25 (22)
[37] ON SEMICLASSICAL GROUND STATES OF A NONLINEAR DIRAC EQUATION
Ding, Yanheng
Liu, Xiaoying
REVIEWS IN MATHEMATICAL PHYSICS, 2012, 24 (10)
[38] STRONGLY LOCALIZED SEMICLASSICAL STATES FOR NONLINEAR DIRAC EQUATIONS
Bartsch, Thomas
Xu, Tian
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2021, 41 (01) : 29 - 60
[39] Splitting methods for nonlinear Dirac equations with Thirring type interaction in the nonrelativistic limit regime
Kraemer, Patrick
Schratz, Katharina
Zhao, Xiaofei
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2021, 387
[40] Nonrelativistic Limit of Ground State Solutions for Nonlinear Dirac-Klein-Gordon Systems
Dong, Xiaojing
Tang, Zhongwei
MINIMAX THEORY AND ITS APPLICATIONS, 2022, 7 (02): : 253 - 276

← 1 2 3 4 5 →