Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4615360 | Journal of Mathematical Analysis and Applications | 2015 | 28 Pages |
Abstract
Explicit solutions are obtained for a class of semilinear radial Schrödinger equations with power nonlinearities in multi-dimensions. These solutions include new similarity solutions and other new group-invariant solutions, as well as new solutions that are not invariant under any symmetries of this class of equations. Many of the solutions have interesting analytical behavior connected with blow-up and dispersion. Several interesting nonlinearity powers arise in these solutions, including the case of the critical (pseudo-conformal) power. In contrast, standard symmetry reduction methods lead to nonlinear ordinary differential equations for which few if any explicit solutions can be derived by standard integration methods.
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Physical Sciences and Engineering
Mathematics
Analysis
Authors
Stephen C. Anco, Wei Feng, Thomas Wolf,