Two new reductions methods for polynomial differential equations and applications to nonlinear PDEs

作者：

Highlights：

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• Two new methods to reduce polynomial equations to first-order equations are provided.

• The procedure is applied to find new exact solutions for nonlinear PDEs.

• Computer algebra codes to obtain the reduced equations are included.

摘要

•Two new methods to reduce polynomial equations to first-order equations are provided.•The procedure is applied to find new exact solutions for nonlinear PDEs.•Computer algebra codes to obtain the reduced equations are included.

论文关键词：34A05,34C14,34C20,34G20,Polynomial ordinary differential equations,First-order reductions,Exact solutions for partial differential equations in mathematical physics

论文评审过程：Received 17 May 2017, Revised 16 October 2017, Accepted 16 October 2017, Available online 21 November 2017, Version of Record 21 November 2017.

论文官网地址：https://doi.org/10.1016/j.cam.2017.10.025