# American Institute of Mathematical Sciences

August  2018, 11(4): 577-582. doi: 10.3934/dcdss.2018032

## Exact solutions of nonlinear partial differential equations

 1 Department of Electrical and Systems Engineering, Washington University, St. Louis, MO 63130, USA

* Corresponding author: Barbara Abraham-Shrauner

Received  November 2016 Revised  May 2017 Published  November 2017

Tests for determination of which nonlinear partial differential equations may have exact analytic nonlinear solutions of any of two types of hyperbolic functions or any of three types of Jacobian elliptic functions are presented. The Power Index Method is the principal method employed that extends the calculation of the power index for the most nonlinear terms to all terms in the nonlinear partial differential equations. An additional test is the identification of the net order of differentiation of each term in the nonlinear differential equations. The nonlinear differential equations considered are evolution equations. The tests extend the homogeneous balance condition that is necessary to conditions that may only be sufficient but are very simple to apply. Superposition of Jacobian elliptic functions is also presented with the introduction of a new basis that simplifies the calculations.

Citation: Barbara Abraham-Shrauner. Exact solutions of nonlinear partial differential equations. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 577-582. doi: 10.3934/dcdss.2018032
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