1992 | OriginalPaper | Buchkapitel
Solutions of Nonlinear Wave Equations and Localization Theory
verfasst von : Walter Craig, C. Eugene Wayne
Erschienen in: Mathematical Physics X
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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In this note we describe a new method for constructing time periodic solutions of nonlinear wave equations of the form (1)$$ {u_{{tt}}} = {u_{{xx}}} - g\left( {x,u} \right)\quad 0 < x < \pi $$, with either periodic or Dirichlet boundary conditions. For a complete description of the results and methods with detailed proofs, see [2]. This article will attempt only to explain the general ideas behind this method and some of its possible extensions.