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Existence and local uniqueness of normalized solutions for two-component Bose–Einstein condensates
In this paper, we consider the following two-component Bose–Einstein condensates (BEC) - Δ u 1 + V 1 ( x ) u 1 = a 1 u 1 3 + μ u 1 + β u 1 u 2 2 in R 2 , - Δ u 2 + V 2 ( x ) u 2 = a 2 u 2 3 + μ u 2 + β u 1 2 u 2 in R 2 , with the constraint ∫ R 2 ( u 1 2 + u 2 2 ) d x = 1 . The existence and local u...
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| Published in: | Zeitschrift für angewandte Mathematik und Physik 2021-12, Vol.72 (6), Article 189 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Citations: | Items that this one cites Items that cite this one |
| Online Access: | Get full text |
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| Summary: | In this paper, we consider the following two-component Bose–Einstein condensates (BEC)
-
Δ
u
1
+
V
1
(
x
)
u
1
=
a
1
u
1
3
+
μ
u
1
+
β
u
1
u
2
2
in
R
2
,
-
Δ
u
2
+
V
2
(
x
)
u
2
=
a
2
u
2
3
+
μ
u
2
+
β
u
1
2
u
2
in
R
2
,
with the constraint
∫
R
2
(
u
1
2
+
u
2
2
)
d
x
=
1
. The existence and local uniqueness of
k
-peak solutions are given by finite-dimensional reduction and local Pohozaev identities, which gives the description of excited state of BEC phenomenon stated and generalizes the results in [
15
] about the ground states. |
|---|---|
| ISSN: | 0044-2275 1420-9039 |
| DOI: | 10.1007/s00033-021-01619-2 |