Solutions of the system of d'Alembert and eikonal equations, and classification of reductions of PDEs

Yehorchenko, Irina

doi:10.1088/1742-6596/621/1/012018

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2019

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“…The criterion of "nonclassical" invariance was firstly formulated in [19] and the rigorous theory of the nonclassical reduction method, theory of reduction modules, was recently developed in [6]. The nonclassical reduction operators are also called nonclassical symmetries [36], conditional symmetries [29] and Q-conditional symmetries [17] (see the related discussion in [28] and some more research papers of interest [14,15,21,33,37,62]).…”

Section: Introductionmentioning

confidence: 99%

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

Vaneeva

Boyko

Zhalij

et al. 2019

Journal of Mathematical Analysis and Applications

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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.

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