Dergiler / Results in Nonlinear Analysis / 2019 / Cilt: 2 - Sayı: 4

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

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

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

Sayfa
182–192
DOI
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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 postcritical Rayleigh-Benard convection by the space-time tardily varying amplitudes while ZEE equationexplains the evolution of a grove population. Some novel complex and real-valued exact solutions for theequations under consideration are presented. Using a new conservation theorem, we construct conservationlaws for the ZEE equation. The physical expression for some of the solutions is presented to shedmore light on the mechanism of the solutions.