Solitary Wave Solutions for the Nonlinear Dirac Equations

2008/12/12 by Meijiao Guan, Guan, Meijiao
Mathematics · #35Q51 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #math.AP #math.DS #msc:35Q51

paper · pdf · doi:10.48550/arxiv.0812.2273

18 pages

arxiv created 2008/12/12 · arxiv updated 2009/12/01

Abstract

In this paper we prove the existence and local uniqueness of stationary states for the nonlinear Dirac equation i ∑_j=0³ \ga^j \pd_j ψ- mψ+ F(ψψ)ψ=0 where m >0 and F(s) = |s|^θ for 1≤ θ< 2. More precisely we show that there exists \e₀ > 0 such that for ω∈(m - \e₀, m), there exists a solution ψ(t,x) = e^-iωtϕ_ω(x), x₀ = t, x = (x₁, x₂, x₃), and the mapping from ω to ϕ_ω is continuous. We prove this result by relating the stationary solutions to the ground states of nonlinear Schrödinger equations.

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