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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:427

Article

Anco, Stephen C.¹  Feng, Wei^1,2  Wolf, Thomas¹ 

[1] Brock Univ, Dept Math & Stat, St Catharines, ON L2S 3A1, Canada

[2] Zhejiang Univ Technol, Dept Math, Hangzhou 310023, Zhejiang, Peoples R China

关键词: Symmetry group;    Exact solutions;    Semilinear Schrodinger equation;    Group foliation;   

DOI  :  10.1016/j.jmaa.2015.02.058

来源: Elsevier

【 摘 要 】

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 ordinary differential equations for which few if any explicit solutions can be derived by standard integration methods. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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