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) |
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Hauptverfasser: | , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
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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. |
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ISSN: | 1050-6926 1559-002X |
DOI: | 10.1007/s12220-022-01117-5 |