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Symmetry 2018, 10(3), 76; https://doi.org/10.3390/sym10030076

Analytic Solutions of Nonlinear Partial Differential Equations by the Power Index Method

Department of Electrical and Systems Engineering, Washington University, St. Louis, MO 63130, USA
Received: 6 February 2018 / Revised: 1 March 2018 / Accepted: 16 March 2018 / Published: 19 March 2018
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Abstract

An updated Power Index Method is presented for nonlinear differential equations (NLPDEs) with the aim of reducing them to solutions by algebraic equations. The Lie symmetry, translation invariance of independent variables, allows for traveling waves. In addition discrete symmetries, reflection, or 180 ° rotation symmetry, are possible. The method tests whether certain hyperbolic or Jacobian elliptic functions are analytic solutions. The method consists of eight steps. The first six steps are quickly applied; conditions for algebraic equations are more complicated. A few exceptions to the Power Index Method are discussed. The method realizes an aim of Sophus Lie to find analytic solutions of nonlinear differential equations. View Full-Text
Keywords: nonlinear; partial differential equations; symmetries; analytic solutions nonlinear; partial differential equations; symmetries; analytic solutions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Abraham-Shrauner, B. Analytic Solutions of Nonlinear Partial Differential Equations by the Power Index Method. Symmetry 2018, 10, 76.

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