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

Abstract

The present study provides an investigation of the Newel-Whitehead-Segel (NWS) and Zeldovich equations

(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

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