The relation between the size of perturbations and the dimension of tori in an infinite-dimensional KAM theorem of Pöschel

2020 ◽  
Vol 197 ◽  
pp. 111754 ◽  
Author(s):  
Xuemei Li ◽  
Shujuan Liu
Keyword(s):  
Kam Theorem ◽  
Infinite Dimensional

Quasi-Periodic Solutions of Nonlinear Wave Equation with x-Dependent Coefficients

2015 ◽  
Vol 25 (03) ◽  
pp. 1550043 ◽  
Author(s):  
Yixian Gao ◽  
Weipeng Zhang ◽  
Shuguan Ji
Keyword(s):  
Wave Equation ◽  
Normal Form ◽  
Periodic Solutions ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Seismic Waves ◽  
Birkhoff Normal Form ◽  
General Boundary Conditions ◽  
Kam Theorem ◽  
Infinite Dimensional

This paper is devoted to the study of quasi-periodic solutions of a nonlinear wave equation with x-dependent coefficients. Such a model arises from the forced vibration of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. Based on the partial Birkhoff normal form and an infinite-dimensional KAM theorem, we can obtain the existence of quasi-periodic solutions for this model under the general boundary conditions.

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