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ВИДЕОТЕКА |
Международная конференция «Геометрические методы в математической физике»
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The solutions of the heat and Burgers equations in terms of elliptic sigma functions V. M. Buchstaber Steklov Mathematical Institute of the Russian Academy of Sciences |
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Аннотация: The algebra of differential operators along Using the Cole-Hopf transformation and our solutions of the heat equation, we obtain solutions of the Burgers equation in terms of Weierstrass functions. The explicit formulas for the differentiation of this solutions by the initial data are obtained. We show that the function $\phi (z,\tau )=\sigma (z;g_{2}(\tau ),g_{3}(\tau ))$ is a solution of the equation \begin{equation*} 8\dot{\phi}=4\phi ^{\prime \prime }+u(\tau )z^{2}\phi \end{equation*} with The natural problem to describe solutions of the heat and Burgers equations in terms of solutions of the previous differential equation with Results presented in the talk were obtained in recent joint works with E.Yu. Bunkova. Main definitions will be introduced during the talk. Язык доклада: английский |