Quasi-periodic Solutions for a Generalized Higher-Order Boussinesq Equation
In this paper one-dimensional generalized eighth-order Boussinesq equation u tt - ∂ x 2 u + β ∂ x 4 u - ∂ x 6 u + ∂ x 8 u + ( u 3 ) xx = 0 , β = ± 1 with the boundary conditions u ( 0 , t ) = u ( π , t ) = u xx ( 0 , t ) = u xx ( π , t ) = u xxxx ( 0 , t ) = u xxxx ( π , t ) = 0 is considered. It is...
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| Veröffentlicht in: | Qualitative theory of dynamical systems 2023-12, Vol.22 (4), Article 139 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper one-dimensional generalized eighth-order Boussinesq equation
u
tt
-
∂
x
2
u
+
β
∂
x
4
u
-
∂
x
6
u
+
∂
x
8
u
+
(
u
3
)
xx
=
0
,
β
=
±
1
with the boundary conditions
u
(
0
,
t
)
=
u
(
π
,
t
)
=
u
xx
(
0
,
t
)
=
u
xx
(
π
,
t
)
=
u
xxxx
(
0
,
t
)
=
u
xxxx
(
π
,
t
)
=
0
is considered. It is proved that the above equation admits small-amplitude quasi-periodic solutions. The proof is based on an infinite dimensional KAM theorem and Birkhoff normal form. |
|---|---|
| ISSN: | 1575-5460 1662-3592 |
| DOI: | 10.1007/s12346-023-00840-w |