Lower dimensional invariant tori with prescribed frequency for nonlinear wave equation (Q603720)
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scientific article; zbMATH DE number 5813555
| Language | Label | Description | Also known as |
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| English | Lower dimensional invariant tori with prescribed frequency for nonlinear wave equation |
scientific article; zbMATH DE number 5813555 |
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Lower dimensional invariant tori with prescribed frequency for nonlinear wave equation (English)
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8 November 2010
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The authors investigate one-dimensional nonlinear wave equation \(u_{tt}-u_{xx}+mu+u^3=0\) for a class and show to admit a Whitney smooth family of small-amplitude quasi-periodic solutions with \(b\)-dimensional Diophantine frequencies based on a partial Birkhoff normal form reduction and an improved KAM method.
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wave equation
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Hamiltonian system
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Birkhoff normal form
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KAM theory
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invariant tori
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small-amplitude quasi-periodic solution
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tangential frequencies mapping
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