
PresentationsFinitedimensional dynamics and exact solutions of the BurgersHuxley equationMoscow State University, Department of Physics, Department of Physical and Mathematical Methods of Control The report presents a new approach to constructing exact solutions of the BurgersHuxley equations. The Burgers  Huxley equation $u_t+uu_x=u_{xx}+f(u)$ is known in various fields of applied mathematics. For example, it describes transport processes in systems when diffusion and convection are equally important. It is usually assumed that the function $f$ is a polynomial of the second or third degree. This allowed us to construct new exact solutions even in the cases when the equation does not have the necessary algebra of symmetries. The theory of finitedimensional dynamics is a natural development of the theory of dynamical systems. Its methods make it possible to construct finitedimensional submanifolds in an infinitedimensional space among solutions of the equations. Elements of these submanifolds are numerated by the solutions of ordinary differential equations.
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