Simple solutions of the Burgers and Hopf equations
- Autores: Beloshapka V.K.1,2
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Afiliações:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Moscow Center for Fundamental and Applied Mathematics
- Edição: Volume 85, Nº 3 (2021)
- Páginas: 5-12
- Seção: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133838
- DOI: https://doi.org/10.4213/im9051
- ID: 133838
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Resumo
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.
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Sobre autores
Valerii 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
Bibliografia
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- V. K. Beloshapka, “Stabilizer of a function in the Gage group”, Russ. J. Math. Phys, 24:2 (2017), 148–152
- 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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