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A KAM theorem with applications to partial equations of higher dimension

Xiaoping Yuan
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Abstract

The existence of lower dimensional KAM tori is shown for a class of nearly integrable Hamiltonian systems where the second Melnikov's conditions are eliminated. As a consequence, it is proved that there exist many invariant tori and thus quasi-periodic solutions for nonlinear wave equations, Schrödinger equations and other equations of higher spatial dimension.

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Xiaoping Yuan. 2006-06-19. A KAM theorem with applications to partial equations of higher dimension. https://doi.org/10.1007/s00220-007-0287-2

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