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

Chengming Cao; Xiaoping Yuan

paper

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

arXiv:1610.09859

Abstract

{\bf Abstract}: The existence of 2-dimensional KAM tori is proved for the perturbed generalized nonlinear vibrating string equation with singularities $u_{tt} = ((1 - x^{2}) u_{x})_{x} - m u - u^{3}$ 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.