Construction of periodic solutions of nonlinear wave equations with Dirichlet boundary conditions by the Lindstedt series method
The existence of periodic solutions is shown for nonlinear wave equations (like the Klein-Gordon and sine-Gordon equations) of the form \(u_{tt}-u_{xx}+\mu u=f(u)\) with Dirichlet boundary value conditions, where \(\mu\) is a positive real number and \(f\) is odd and analytic. A renormalized Lindstedt series is used and renormalized group methods are applied to show their convergence.
scientific article; zbMATH DE number 2118446