Simple solutions of the Burgers and Hopf equations

Abstract

Abstract We describe all solutions of the Burgers equation of analytic complexity not exceeding . It turns out that all such solutions fall into four families of dimensions not exceeding that are represented by elementary functions. An example of a family of solutions of the Burgers equation of complexity is given. A similar problem is also solved for the Hopf equation. It turns out that all solutions to the Hopf equation of complexity form a two-parameter family of fractional-linear functions which coincides with one of the families of solutions of the Burgers equation.