Notes on symplectic non-squeezing of the KdV flow
نویسندگان
چکیده
منابع مشابه
Symplectic Non-squeezing of the Kdv Flow
We prove two finite dimensional approximation results and a symplectic non-squeezing property for the Korteweg-de Vries (KdV) flow on the circle T. The nonsqueezing result relies on the aforementioned approximations and the finite-dimensional nonsqueezing theorem of Gromov [13]. Unlike the work of Kuksin [21] which initiated the investigation of non-squeezing results for infinite dimensional Ha...
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15 صفحه اولNotes on Symplectic Geometry
1. Week 1 1 1.1. The cotangent bundle 1 1.2. Geodesic flow as Hamiltonian flow 4 2. Week 2 7 2.1. Darboux’s theorem 7 3. Week 3 10 3.1. Submanifolds of symplectic manifolds 10 3.2. Contact manifolds 12 4. Week 4 15 4.1. Symplectic linear group and linear complex structures 15 4.2. Symplectic vector bundles 18 5. Week 5 21 5.1. Almost complex manifolds 21 5.2. Kähler manifolds 24 6. Week 6 26 6....
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We examine some symplectic and multisymplectic methods for the notorious Korteweg–de Vries equation, with the question whether the added structure preservation that these methods offer is key in providing high quality schemes for the long time integration of nonlinear, conservative partial differential equations. Concentrating on 2nd order discretizations, several interesting schemes are constr...
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ژورنال
عنوان ژورنال: Journées Équations aux dérivées partielles
سال: 2005
ISSN: 0752-0360
DOI: 10.5802/jedp.25