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- W145769863 abstract "Introduction1 Some analysis in Hilbert spaces and scales1.1 Smooth and analytic maps1.2 Scales of Hilbert spaces and interpolation1.3 Differential forms2 Symplectic structures and Hamiltonian equations2.1 Basic definitions2.2 Symplectic transformations2.3 Darboux lemmasAppendix. Time-quasiperiodic solutions3 Lax-integrable Hamiltonian equations and their integrable subsystems3.1 Examples of Hamiltonian PDEs3.2 Lax-integrable equations3.3 Integrable subsystems4 Finite-gap manifolds and theta-formulas4.1 Finite-gap manifolds for the KdV equation4.2 The Its-Matveev theta-formulas4.3 Higher equations from the KdV hierarchy4.4 Sine-Gordon equation under Dirichlet boundary conditions5 Linearised equations and their Floquet solutions5.1 The linearised equation5.2 Floquet solutions5.3 Complete systems of Floquet solutions5.4 Lower-dimensional invariant tori of finite-dimensional systems and Floquet’s theorem6 Linearised Lax-integrable equations6.1 Abstract situation6.2 Linearised KdV equation6.3 Higher KdV-equations6.4 Linearised SG equation7 Normal form7.1 A normal form theorem7.2 Examples8 The KAM theorem8.1 The main theorem and related results8.2 Reduction to a parameter-depending case8.3 A KAM-theorem for parameter-depending equations8.4 Completion of the Main Theorem’s proof (Step 4)9 Examples9.1 Perturbed KdV equation9.2 Higher KdV equations9.3 Perturbed SG equation9.4 KAM-persistence of lower-dimensional invariant tori of nonlinear finite-dimensional systemsReferences" @default.
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- W145769863 date "2004-10-12" @default.
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- W145769863 title "KAM-persistence of finite-gap solutions" @default.
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