ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

The Tanh-function Method and the (G'/G)-expansion Method for the Kinetic Mckean System


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.



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