A modification to the first integral method and its applications
作者：
Highlights：
• Our modified first integral method enlarges original first integral method to higher-order ordinary differential equations, and in the meantime compared with original first integral method, our modification is very straight and easy to calculate when we deal with second order ordinary differential equation.
• Some important first integrals are straightly reobtained for the density-dependent conformable fractional diffusion-reaction equation, the famous Duffing-van der Pol oscillator, and the well-known nonlinear evolution equation for description of surface waves in a convecting liquid.
• Novel first integrals are obtained for the complex cubic-quintic Ginzburg–Landau equation and the KdV–Burgers–Fisher equation.
摘要
•Our modified first integral method enlarges original first integral method to higher-order ordinary differential equations, and in the meantime compared with original first integral method, our modification is very straight and easy to calculate when we deal with second order ordinary differential equation.•Some important first integrals are straightly reobtained for the density-dependent conformable fractional diffusion-reaction equation, the famous Duffing-van der Pol oscillator, and the well-known nonlinear evolution equation for description of surface waves in a convecting liquid.•Novel first integrals are obtained for the complex cubic-quintic Ginzburg–Landau equation and the KdV–Burgers–Fisher equation.
论文关键词：First integral method,Conformable fractional diffusion-reaction equation,Duffing-van der Pol oscillator,Complex cubic-quintic Ginzburg–Landau equation,Equation for surface waves,KdV–Burgers–Fisher equation
论文评审过程：Received 30 January 2019, Revised 3 December 2020, Accepted 3 December 2021, Available online 18 December 2021, Version of Record 18 December 2021.
论文官网地址：https://doi.org/10.1016/j.amc.2021.126855
