A remark on global bifurcations of solutions of Ginzburg–Landau equation
We have proved that all the closed connected sets of solutions of the complex Ginzburg–Landau equation { − Δ u ( x ) + 2 i 〈 A ( x ) , ∇ u ( x ) 〉 + ‖ A ( x ) ‖ 2 u ( x ) = λ ( 1 − | u ( x ) | 2 ) u ( x ) in Ω , u = 0 on ∂ Ω , bifurcating from the set of normal solutions { 0 } × ( 0 , + ∞ ) ⊂ H 0...
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| Veröffentlicht in: | Nonlinear analysis: real world applications 2011-12, Vol.12 (6), p.2943-2946 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | We have proved that all the closed connected sets of solutions of the complex Ginzburg–Landau equation
{
−
Δ
u
(
x
)
+
2
i
〈
A
(
x
)
,
∇
u
(
x
)
〉
+
‖
A
(
x
)
‖
2
u
(
x
)
=
λ
(
1
−
|
u
(
x
)
|
2
)
u
(
x
)
in
Ω
,
u
=
0
on
∂
Ω
,
bifurcating from the set of normal solutions
{
0
}
×
(
0
,
+
∞
)
⊂
H
0
1
(
Ω
,
C
)
×
(
0
,
+
∞
)
are unbounded, where
Ω
⊂
R
2
is an open, bounded domain with smooth boundary,
A
(
x
1
,
x
2
)
=
(
−
x
2
,
x
1
)
and
‖
⋅
‖
is the usual norm in
R
2
. |
|---|---|
| ISSN: | 1468-1218 1878-5719 |
| DOI: | 10.1016/j.nonrwa.2011.04.006 |