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arXiv · 1610.09859

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

Chengming Cao·Xiaoping Yuan
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Abstract

{\bf Abstract}: 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.

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Chengming Cao, Xiaoping Yuan. 2016-10-31. Quasi-periodic solutions for perturbed generalized nonlinear vibrating string equation with singularities. https://arxiv.org/abs/1610.09859

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