Simple solutions of the Burgers and Hopf equations
- Authors: Beloshapka V.K.1,2
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Affiliations:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Moscow Center for Fundamental and Applied Mathematics
- Issue: Vol 85, No 3 (2021)
- Pages: 5-12
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133838
- DOI: https://doi.org/10.4213/im9051
- ID: 133838
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Abstract
We describe all solutions of the Burgers equation of analytic complexity notexceeding $1$. It turns out that all such solutions fall into four families ofdimensions not exceeding $3$ that are represented by elementary functions. An example of a family of solutions of the Burgers equation of complexity $2$ is given.A similar problem is also solved for the Hopf equation. It turns out that allsolutions to the Hopf equation of complexity $1$ form a two-parameter family offractional-linear functions which coincides with one of the families of solutions ofthe Burgers equation.
About the authors
Valerii Konstantinovich Beloshapka
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Moscow Center for Fundamental and Applied Mathematics
Email: vkb@strogino.ru
Doctor of physico-mathematical sciences, Professor
References
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- В. К. Белошапка, “Простые решения трeх уравнений математической физики”, Тр. ММО, 79, № 2, МЦНМО, М., 2018, 221–236
- М. А. Степанова, “Об аналитической сложности дифференциально-алгебраических функций”, Матем. сб., 210:12 (2019), 120–135
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