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arXiv · 1408.3751

Exact solutions of semilinear radial Schrodinger equations by separation of group foliation variables

Stephen C. Anco·Wei Feng·Thomas Wolf
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Abstract

Explicit solutions are obtained for a class of semilinear radial Schrodinger 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 ODEs for which few if any explicit solutions can be derived by standard integration methods.

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Stephen C. Anco, Wei Feng, Thomas Wolf. 2014-08-16. Exact solutions of semilinear radial Schrodinger equations by separation of group foliation variables. https://arxiv.org/abs/1408.3751

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