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Quasi-periodic solutions for 1D resonant beam equation

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  • In this paper, one--dimensional ($1D$) resonant beam equation

    $u_{t t} +u_{x x x x} +u^3=0,$

    with hinged boundary conditions is considered. It is proved that the above equation admits small-amplitude quasi-periodic solutions corresponding to finite dimensional invariant tori of an associated infinite dimensional dynamical system. The proof is based on infinite dimensional KAM theorem, partial normal form and scaling skills.

    Mathematics Subject Classification: 37K55.


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