Breathers for nonlinear wave equations
Michael W. Smiley (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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The semilinear differential equation (1), (2), (3), in with , (a nonlinear wave equation) is studied. In particular for , the existence is shown of a weak solution , periodic with period , non-constant with respect to , and radially symmetric in the spatial variables, that is of the form . The proof is based on a distributional interpretation for a linear equation corresponding to the given problem, on the Paley-Wiener criterion for the Laplace Transform, and on the alternative...