2019/02/07 by Mahdieh Yourdkhany, Yourdkhany, Mahdieh, Mehdi Nadjafikhah +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Adjoint representation of a Lie algebra #Advanced Topics in Algebra #Algebra over a field #Algebraic number #Applied mathematics #Computer science #Equivalence (formal languages) #Group (periodic table) #Hessian matrix #Invariant (physics) #Lie algebra #Lie conformal algebra #Lie group #Lie theory #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Nonlinear system #Physics #Pure mathematics #Space (punctuation) #Sphingolipid Metabolism and Signaling #math.DG #msc:35A30 #msc:53A55 #msc:53C12 #msc:58J70 #msc:76M60
paper · pdf · doi:10.1007/s41980-020-00424-3
arxiv created 2019/02/07 · arxiv updated 2019/02/08 · crossref issued 2020/07/16 · crossref published 2020/07/16 · crossref published-online 2020/07/16 · openalex publication_date 2020/07/16 · crossref created 2020/07/16 · crossref deposited 2021/07/15 · crossref published-print 2021/08/01 · crossref indexed 2025/02/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the class of 3-dimensional nonlinear 2-hessian equations mentioned in the text. We perform preliminary group classification on 2-hessian equation. In fact, we find additional equivalence transformation on the space (x,y,z,u,f), with the aid of a method, then we take their projections on the space (x,y,z,f), so we prove an optimal system of one-dimensional Lie sub algebras of this equation is generated by A1 to A12, which introduced in theorem 2, ultimately, A number of new interesting nonlinear invariant models are obtained which have non-trivial in variance algebras. The result of these works is a wide class of equations which summarized in table. So at the end of this work, some exact solutions of 2-hessian equation are presented. The paper is one of the few applications of an algebraic approach to the group classification using Lie method.