Symmetry analysis and some new exact solutions of the Newell-Whitehead-Segel and Zeldovich equations

Authors : Abdullahi YUSUF, Behzad GHANBARİ, Sania QURESHİ, Mustafa INC, Dumitru BALEANU

Pages : 182-192

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Publication Date : 2019-12-25

Article Type : Research Paper

Abstract :The present study provides an investigation of the Newel-Whitehead-Segel insert ignore into journalissuearticles values(NWS); and Zeldovich equations insert ignore into journalissuearticles values(ZEE); equation via Lie symmetry analysis and generalize exponential rational function methods. The NWS equation exhibits the relation between a continuous nite bandwidth of modes and a post critical Rayleigh-Benard convection by the space-time tardily varying amplitudes while ZEE equation explains the evolution of a grove population. Some novel complex and real-valued exact solutions for the equations under consideration are presented. Using a new conservation theorem, we construct conservation laws for the ZEE equation. The physical expression for some of the solutions is presented to shed more light on the mechanism of the solutions.
Keywords : Newell Whitehead Segel equation, Zeldovich equation, symmetries