L2-Normalized Solitary Wave Solutions of a Nonlinear Dirac Equation

In this paper, we study the following nonlinear Dirac equation - i ħ ∂ t ψ = i c ħ ∑ k = 1 3 α k ∂ k ψ - m c 2 β ψ + K ( x ) | ψ | p - 2 ψ , ( N D E ) where ψ : R × R 3 → C 4 , K ∈ L ∞ ( R 3 ) , c denotes the speed of light, m > 0 , the mass of the electron, ħ is Planck’s constant, ∂ k = ∂ ∂ x k...

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Veröffentlicht in:The Journal of geometric analysis 2023, Vol.33 (2)
Hauptverfasser: Ding, Yanheng, Yu, Yuanyang, Zhao, Fukun
Format: Artikel
Sprache:eng
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Zusammenfassung:In this paper, we study the following nonlinear Dirac equation - i ħ ∂ t ψ = i c ħ ∑ k = 1 3 α k ∂ k ψ - m c 2 β ψ + K ( x ) | ψ | p - 2 ψ , ( N D E ) where ψ : R × R 3 → C 4 , K ∈ L ∞ ( R 3 ) , c denotes the speed of light, m > 0 , the mass of the electron, ħ is Planck’s constant, ∂ k = ∂ ∂ x k , α 1 , α 2 , α 3 , β are 4 × 4 Pauli–Dirac matrices and p ∈ ( 2 , 8 3 ) . We present a new approach which is based on a perturbation argument and show the existence of L 2 -normalized solitary wave solutions of (NDE) using variational methods.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-022-01117-5