Exact solutions of semilinear radial wave equations in n dimensions
Anco, Stephen C. ; Liu, Sheng
arXiv, 0309049 / Harvested from arXiv
Text on arXiv
Exact solutions are derived for an n-dimensional radial wave equation with a general power nonlinearity. The method, which is applicable more generally to other nonlinear PDEs, involves an ansatz technique to solve a first-order PDE system of group-invariant variables given by group foliations of the wave equation, using the one-dimensional admitted point symmetry groups. (These groups comprise scalings and time translations, admitted for any nonlinearity power, in addition to space-time inversions admitted for a particular conformal nonlinearity power). This is shown to yield not only group-invariant solutions as derived by standard symmetry reduction, but also other exact solutions of a more general form. In particular, solutions with interesting analytical behavior connected with blow ups as well as static monopoles are obtained.
Publié le : 2003-09-19
Classification:  Mathematical Physics 
@article{0309049,
     author = {Anco, Stephen C. and Liu, Sheng},
     title = {Exact solutions of semilinear radial wave equations in n dimensions},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0309049}
}

Anco, Stephen C.; Liu, Sheng. Exact solutions of semilinear radial wave equations in n dimensions. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0309049/