KAM tori for reversible partial differential equations

• Published in: Nonlinearity Vol. 24; no. 4; pp. 1189 - 1228
• Main Authors: Zhang, Jing, Gao, Meina, Yuan, Xiaoping
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.04.2011; Institute of Physics
• Subjects: Boundary conditions; Derivatives; Dirichlet problem; Exact sciences and technology; Global analysis, analysis on manifolds; Mathematical analysis; Mathematical methods in physics; Mathematics; Nonlinearity; Numerical analysis; Numerical analysis. Scientific computation; Other topics in mathematical methods in physics; Partial differential equations; Partial differential equations, boundary value problems; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; Physics; Sciences and techniques of general use; Theorems; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Toruses; Non linear equation; Nonlinear analysis; Derivative; Perturbation; Infinite system; Boundary condition; KAM theorem; Partial differential equation; Mathematical physics

In this paper, we establish a KAM theorem for an infinite dimensional reversible system with unbounded perturbation, by which we obtain quasi-periodic solutions of a class of nonlinear Schodinger equations with a derivative in nonlinear terms, subject to Dirichlet boundary conditions.