Geodesic
Simple solutions of the Burgers and Hopf equations
Izvestiya. Mathematics , Tome 85 (2021) no. 3, pp. 343-350

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We describe all solutions of the Burgers equation of analytic complexity not exceeding $1$. It turns out that all such solutions fall into four families of dimensions 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 all solutions to the Hopf equation of complexity $1$ form a two-parameter family of fractional-linear functions which coincides with one of the families of solutions of the Burgers equation.
Keywords: analytic complexity, special functions, analytic spectrum. 
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     author = {V. K. Beloshapka},
     title = {Simple solutions of the {Burgers} and {Hopf} equations},
     journal = {Izvestiya. Mathematics },
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     number = {3},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2021_85_3_a1/}
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V. K. Beloshapka. Simple solutions of the Burgers and Hopf equations. Izvestiya. Mathematics , Tome 85 (2021) no. 3, pp. 343-350. http://geodesic.mathdoc.fr/item/IM2_2021_85_3_a1/