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Quasi-periodic solutions for perturbed generalized nonlinear vibrating string equation with singularities

  • Author Bio: E-mail address: 12110180001@fudan.edu.cn; E-mail address: xpyuan@fudan.edu.cn
Supported by NNSFC 11271076 and NNSFC 11121101.
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  • The existence of 2-dimensional KAM tori is proved for the perturbed generalized nonlinear vibrating string equation with singularities $u_{tt}=((1-x^2)u_x)_x-mu-u^3$ subject to certain boundary conditions by means of infinite-dimensional KAM theory with the help of partial Birkhoff normal form, the characterization of the singular function space and the estimate of the integrals related to Legendre basis.

    Mathematics Subject Classification: 37K55.


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