English

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

Mathematical Physics 2019-08-13 v2 Analysis of PDEs math.MP Exactly Solvable and Integrable Systems

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.

Keywords

Cite

@article{arxiv.1809.05022,
  title  = {Classification of reduction operators and exact solutions of variable coefficient Newell-Whitehead-Segel equations},
  author = {Olena Vaneeva and Vyacheslav Boyko and Alexander Zhalij and Christodoulos Sophocleous},
  journal= {arXiv preprint arXiv:1809.05022},
  year   = {2019}
}

Comments

12 pages, to appear in the Journal of Mathematical Analysis and Applications