Classification of reduction operators and exact solutions of variable coefficient Newell-Whitehead-Segel equations

TL;DR

This paper classifies reduction operators for variable coefficient Newell-Whitehead-Segel equations, derives criteria for their reducibility to constant coefficient forms, and constructs wide families of exact solutions.

Contribution

It provides a comprehensive classification of symmetry operators and criteria for reducibility, along with explicit exact solutions for these equations.

Findings

Classification of Lie and nonclassical reduction operators

Explicit criteria for reducibility to constant coefficients

Construction of wide families of exact solutions

Abstract

A class of the Newell-Whitehead-Segel equations (also known as generalized Fisher equations and Newell-Whitehead equations) is studied with Lie and "nonclassical" symmetry points of view. The classifications of Lie reduction operators and of regular nonclassical reduction operators are performed. The set of admissible transformations (the equivalence groupoid) of the class is described exhaustively. The criterion of reducibility of variable coefficient Newell-Whitehead-Segel equations to their constant coefficient counterparts is derived. Wide families of exact solutions for such variable coefficient equations are constructed.