Simple solutions of the Burgers and Hopf equations
- 作者: Beloshapka V.1,2
-
隶属关系:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Moscow Center for Fundamental and Applied Mathematics
- 期: 卷 85, 编号 3 (2021)
- 页面: 5-12
- 栏目: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133838
- DOI: https://doi.org/10.4213/im9051
- ID: 133838
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详细
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.
作者简介
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
参考
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