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Русская версия

**Sergei Anatolievich Dukhnovsky**

Candidate of Physico-Mathematical Sciences

Moscow State University of Civil Engineering

Department of Applied Mathematics

Yaroslavskoye Shosse 26,

129337 Moscow, Russia

In this paper, we consider the discrete kinetic McKean system. The McKean system is the Boltzmann kinetic equation, and for this model momentum and energy are not conserved. For the first time, new traveling wave solutions are found using the tanh-function method, the extended tanh-function method and the (G'/G)-expansion method. These methods are a powerful, reliable and effective tool for finding exact solutions to nonlinear partial differential equations in mathematical physics and engineering fields. With the help of computerized symbolic computation, we obtain kink waves, singular kink waves, periodic waves and rational solutions. Similarly, it is possible to find exact solutions for other kinetic models.

- Knudsen number
- McKean system
- symbolic computation
- tanh-function method
- traveling wave solutions

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