E.A. Zhukova 1, A.A. Kutukov, N.A. Kudryashov
Department of Applied Mathematics and Computer Science, Institute of Laser and Plasma Technologies, National Research Nuclear University ”Moscow Engineering Physics Institute”, 115409, Moscow, Russia
Received 01 August 2025; accepted in revised form 05 September 2025
Abstract: The hierarchy of Burgers equations is considered. Using self-similar variables the hierarchy of ordinary differential equations is derived. Analytical solutions for ordinary differential equations, expressed in terms of a generalized hypergeometric function, are found. The Cauchy problem for a hierarchy of ordinary differential equations is considered.
A relationship is found between solutions expressed in terms of a hypergeometric function and generalized Hermite polynomials. Direct transformation methods and mathematical induction were used in this work. The analytical solutions can provide benchmarks for validating numerical algorithms and assessing the convergence of computational schemes.
© 2025 European Society of Computational Methods in Sciences and Engineering
Keywords: Burgers hierarchy, hypergeometric functions, ordinary differential equation, Cole-Hopf transformation, group transformations
Mathematics Subject Classification: 35D99