Breathers for nonlinear wave equations

Smiley, Michael W.. "Breathers for nonlinear wave equations." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 82.3 (1988): 431-435. <http://eudml.org/doc/289089>.

@article{Smiley1988,
abstract = {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.},
author = {Smiley, Michael W.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
keywords = {Periodicity; Breathers; Distributional solution; Weighted Hilbert space; Method of alternative problems},
language = {eng},
month = {9},
number = {3},
pages = {431-435},
publisher = {Accademia Nazionale dei Lincei},
title = {Breathers for nonlinear wave equations},
url = {http://eudml.org/doc/289089},
volume = {82},
year = {1988},
}

TY - JOUR
AU - Smiley, Michael W.
TI - Breathers for nonlinear wave equations
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1988/9//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 3
SP - 431
EP - 435
AB - 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.
LA - eng
KW - Periodicity; Breathers; Distributional solution; Weighted Hilbert space; Method of alternative problems
UR - http://eudml.org/doc/289089
ER -