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 selfinteractions 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 ^{–iω1t}R _{1}cosθ,R _{1}sinθΦ=e ^{–iω2t}R _{2}cosη,R _{2}sinη, 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:
 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):
 LAUR1621471
Journal ID: ISSN 03759601; TRN: US1700910
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physics Letters. A
 Additional Journal Information:
 Journal Volume: 381; Journal Issue: 12; Journal ID: ISSN 03759601
 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 selfinteractions 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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