Scattering of solitons for Dirac equation coupled to a particle

A. I. Komech; E. A. Kopylova; H. Spohn

doi:10.1016/j.jmaa.2011.05.037

Scattering of solitons for Dirac equation coupled to a particle

A. I. Komech, E. A. Kopylova, H. Spohn

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Abstract

We establish soliton-like asymptotics for finite energy solutions to the Dirac equation coupled to a relativistic particle. Any solution with initial state close to the solitary manifold, converges in long time limit to a sum of traveling wave and outgoing free wave. The convergence holds in global energy norm. The proof uses spectral theory and symplectic projection onto solitary manifold in the Hilbert phase space.

Original language	English
Pages (from-to)	265-290
Number of pages	26
Journal	Journal of Mathematical Analysis and Applications
Volume	383
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2011.05.037
State	Published - 15 Nov 2011

Keywords

Dirac equation
Long-time asymptotics
Modulation equations
Solitary manifold
Soliton
Symplectic projection

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10.1016/j.jmaa.2011.05.037

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@article{303926ff1e554d14906f4ed7a90f5418,

title = "Scattering of solitons for Dirac equation coupled to a particle",

abstract = "We establish soliton-like asymptotics for finite energy solutions to the Dirac equation coupled to a relativistic particle. Any solution with initial state close to the solitary manifold, converges in long time limit to a sum of traveling wave and outgoing free wave. The convergence holds in global energy norm. The proof uses spectral theory and symplectic projection onto solitary manifold in the Hilbert phase space.",

keywords = "Dirac equation, Long-time asymptotics, Modulation equations, Solitary manifold, Soliton, Symplectic projection",

author = "Komech, {A. I.} and Kopylova, {E. A.} and H. Spohn",

note = "Funding Information: E-mail addresses: [email protected] (A.I. Komech), [email protected] (E.A. Kopylova), [email protected] (H. Spohn). 1 Supported partly by Alexander von Humboldt Research Award. 2 Supported partly by grants of FWF, DFG and RFBR.",

year = "2011",

month = nov,

day = "15",

doi = "10.1016/j.jmaa.2011.05.037",

language = "English",

volume = "383",

pages = "265--290",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

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TY - JOUR

T1 - Scattering of solitons for Dirac equation coupled to a particle

AU - Komech, A. I.

AU - Kopylova, E. A.

AU - Spohn, H.

N1 - Funding Information: E-mail addresses: [email protected] (A.I. Komech), [email protected] (E.A. Kopylova), [email protected] (H. Spohn). 1 Supported partly by Alexander von Humboldt Research Award. 2 Supported partly by grants of FWF, DFG and RFBR.

PY - 2011/11/15

Y1 - 2011/11/15

N2 - We establish soliton-like asymptotics for finite energy solutions to the Dirac equation coupled to a relativistic particle. Any solution with initial state close to the solitary manifold, converges in long time limit to a sum of traveling wave and outgoing free wave. The convergence holds in global energy norm. The proof uses spectral theory and symplectic projection onto solitary manifold in the Hilbert phase space.

AB - We establish soliton-like asymptotics for finite energy solutions to the Dirac equation coupled to a relativistic particle. Any solution with initial state close to the solitary manifold, converges in long time limit to a sum of traveling wave and outgoing free wave. The convergence holds in global energy norm. The proof uses spectral theory and symplectic projection onto solitary manifold in the Hilbert phase space.

KW - Dirac equation

KW - Long-time asymptotics

KW - Modulation equations

KW - Solitary manifold

KW - Soliton

KW - Symplectic projection

UR - http://www.scopus.com/inward/record.url?scp=80955177584&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2011.05.037

DO - 10.1016/j.jmaa.2011.05.037

M3 - Article

AN - SCOPUS:80955177584

SN - 0022-247X

VL - 383

SP - 265

EP - 290

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Scattering of solitons for Dirac equation coupled to a particle

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Keywords

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