Nonlinear Dirac equation on graphs with localized nonlinearities: Bound states and nonrelativistic limit

William Borrelli; Raffaele Carlone; Lorenzo Tentarelli

doi:10.1137/18M1211714

Nonlinear Dirac equation on graphs with localized nonlinearities: Bound states and nonrelativistic limit

William Borrelli, Raffaele Carlone, Lorenzo Tentarelli

Università Cattolica del Sacro Cuore

University of Naples Federico II

Research output: Contribution to journal › Article

10 Citations (Scopus)

Abstract

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 L2-subcritical case, they converge to the bound states of the nonlinear Schrodinger equation in the nonrelativistic limit.

Original language	English
Pages (from-to)	1046-1081
Number of pages	36
Journal	SIAM Journal on Mathematical Analysis
Volume	51
DOIs	https://doi.org/10.1137/18M1211714
Publication status	Published - 2019

Keywords

Bound states
Linking
Metric graphs
Nonlinear Dirac equations
Nonrelativistic limit
Variational methods

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10.1137/18M1211714

Cite this

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title = "Nonlinear Dirac equation on graphs with localized nonlinearities: Bound states and nonrelativistic limit",

abstract = "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 L2-subcritical case, they converge to the bound states of the nonlinear Schrodinger equation in the nonrelativistic limit.",

keywords = "Bound states, Linking, Metric graphs, Nonlinear Dirac equations, Nonrelativistic limit, Variational methods, Bound states, Linking, Metric graphs, Nonlinear Dirac equations, Nonrelativistic limit, Variational methods",

author = "William Borrelli and Raffaele Carlone and Lorenzo Tentarelli",

year = "2019",

doi = "10.1137/18M1211714",

language = "English",

volume = "51",

pages = "1046--1081",

journal = "SIAM Journal on Mathematical Analysis",

issn = "0036-1410",

publisher = "Society for Industrial and Applied Mathematics Publications",

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TY - JOUR

T1 - Nonlinear Dirac equation on graphs with localized nonlinearities: Bound states and nonrelativistic limit

AU - Borrelli, William

AU - Carlone, Raffaele

AU - Tentarelli, Lorenzo

PY - 2019

Y1 - 2019

N2 - 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 L2-subcritical case, they converge to the bound states of the nonlinear Schrodinger equation in the nonrelativistic limit.

AB - 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 L2-subcritical case, they converge to the bound states of the nonlinear Schrodinger equation in the nonrelativistic limit.

KW - Bound states

KW - Linking

KW - Metric graphs

KW - Nonlinear Dirac equations

KW - Nonrelativistic limit

KW - Variational methods

KW - Bound states

KW - Linking

KW - Metric graphs

KW - Nonlinear Dirac equations

KW - Nonrelativistic limit

KW - Variational methods

UR - http://hdl.handle.net/10807/171323

U2 - 10.1137/18M1211714

DO - 10.1137/18M1211714

M3 - Article

SN - 0036-1410

VL - 51

SP - 1046

EP - 1081

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

ER -

Nonlinear Dirac equation on graphs with localized nonlinearities: Bound states and nonrelativistic limit

Abstract

Keywords

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