Geodesic
Breathers for nonlinear wave equations
Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 82 (1988) no. 3, pp. 431-435 Cet article a éte moissonné depuis la source Biblioteca Digitale Italiana di Matematica

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The semilinear differential equation (1), (2), (3), in $\mathbb{R} \times \Omega$ with $\Omega \in \mathbb{R}^{N}$, (a nonlinear wave equation) is studied. In particular for $\Omega = \mathbb{R}^{3}$, the existence is shown of a weak solution $u(t,x)$, periodic with period $T$, non-constant with respect to $t$, and radially symmetric in the spatial variables, that is of the form $u(t,x) = \nu(t,|x|)$. 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 method of Cesari. 
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     author = {Smiley, Michael W.},
     title = {Breathers for nonlinear wave equations},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali},
     pages = {431--435},
     year = {1988},
     volume = {Ser. 8, 82},
     number = {3},
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Smiley, Michael W. Breathers for nonlinear wave equations. Atti della Accademia nazionale dei Lincei. Rendiconti della Classe di scienze fisiche, matematiche e naturali, Série 8, Tome 82 (1988) no. 3, pp. 431-435. http://geodesic.mathdoc.fr/item/RLINA_1988_8_82_3_a4/

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