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Title: Approximate analytic solutions to coupled nonlinear Dirac equations

Abstract

Here, we consider the coupled nonlinear Dirac equations (NLDEs) in 1+11+1 dimensions with scalar–scalar self-interactions g 1 2/2($$\bar{ψ}$$ψ) 2 + g 2 2/2($$\bar{Φ}$$Φ) 2 + g 2 3($$\bar{ψ}$$ψ)($$\bar{Φ}$$Φ) as well as vector–vector interactions g 1 2/2($$\bar{ψ}$$γμψ)($$\bar{ψ}$$γμψ) + g 2 2/2($$\bar{Φ}$$γμΦ)($$\bar{Φ}$$γμΦ) + g 2 3($$\bar{ψ}$$γμψ)($$\bar{Φ}$$γμΦ). Writing the two components of the assumed rest frame solution of the coupled NLDE equations in the form ψ=e –iω1tR 1cosθ,R 1sinθΦ=e –iω2tR 2cosη,R 2sinη, and assuming that θ(x),η(x) have the same functional form they had when g3 = 0, which is an approximation consistent with the conservation laws, we then find approximate analytic solutions for Ri(x) which are valid for small values of g 3 2/g 2 2 and g 3 2/g 1 2. In the nonrelativistic limit we show that both of these coupled models go over to the same coupled nonlinear Schrödinger equation for which we obtain two exact pulse solutions vanishing at x → ±∞.

Authors:
; ORCiD logo;
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1342859
Alternate Identifier(s):
OSTI ID: 1412556
Report Number(s):
LA-UR-16-21471
Journal ID: ISSN 0375-9601; TRN: US1700910
Grant/Contract Number:
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physics Letters. A
Additional Journal Information:
Journal Volume: 381; Journal Issue: 12; Journal ID: ISSN 0375-9601
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Atomic and Nuclear Physics; Mathematics

Citation Formats

Khare, Avinash, Cooper, Fred, and Saxena, Avadh. Approximate analytic solutions to coupled nonlinear Dirac equations. United States: N. p., 2017. Web. doi:10.1016/j.physleta.2017.01.018.
Khare, Avinash, Cooper, Fred, & Saxena, Avadh. Approximate analytic solutions to coupled nonlinear Dirac equations. United States. doi:10.1016/j.physleta.2017.01.018.
Khare, Avinash, Cooper, Fred, and Saxena, Avadh. Mon . "Approximate analytic solutions to coupled nonlinear Dirac equations". United States. doi:10.1016/j.physleta.2017.01.018. https://www.osti.gov/servlets/purl/1342859.
@article{osti_1342859,
title = {Approximate analytic solutions to coupled nonlinear Dirac equations},
author = {Khare, Avinash and Cooper, Fred and Saxena, Avadh},
abstractNote = {Here, we consider the coupled nonlinear Dirac equations (NLDEs) in 1+11+1 dimensions with scalar–scalar self-interactions g12/2($\bar{ψ}$ψ)2 + g22/2($\bar{Φ}$Φ)2 + g23($\bar{ψ}$ψ)($\bar{Φ}$Φ) as well as vector–vector interactions g12/2($\bar{ψ}$γμψ)($\bar{ψ}$γμψ) + g22/2($\bar{Φ}$γμΦ)($\bar{Φ}$γμΦ) + g23($\bar{ψ}$γμψ)($\bar{Φ}$γμΦ). Writing the two components of the assumed rest frame solution of the coupled NLDE equations in the form ψ=e–iω1tR1cosθ,R1sinθΦ=e–iω2tR2cosη,R2sinη, and assuming that θ(x),η(x) have the same functional form they had when g3 = 0, which is an approximation consistent with the conservation laws, we then find approximate analytic solutions for Ri(x) which are valid for small values of g32/g22 and g32/g12. In the nonrelativistic limit we show that both of these coupled models go over to the same coupled nonlinear Schrödinger equation for which we obtain two exact pulse solutions vanishing at x → ±∞.},
doi = {10.1016/j.physleta.2017.01.018},
journal = {Physics Letters. A},
number = 12,
volume = 381,
place = {United States},
year = {Mon Jan 30 00:00:00 EST 2017},
month = {Mon Jan 30 00:00:00 EST 2017}
}

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