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Title: Approximate analytic solutions to coupled nonlinear Dirac equations

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