Approximate analytic solutions to coupled nonlinear Dirac equations

Journal Article · Mon Jan 30 00:00:00 EST 2017 · Physics Letters. A

DOI:https://doi.org/10.1016/j.physleta.2017.01.018· OSTI ID:1342859

Khare, Avinash; Cooper, Fred ; Saxena, Avadh

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 → ±∞.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE Laboratory Directed Research and Development (LDRD) Program
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1342859
• Alternate ID(s): OSTI ID: 1412556
• Report Number(s): LA-UR-16-21471; TRN: US1700910
• Journal Information: Physics Letters. A, Vol. 381, Issue 12; ISSN 0375-9601
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
Atomic and Nuclear Physics
Mathematics