Traveling wave solutions for the two-dimensional Zakharov-Kuznetsov-Burgers equation

Abstract

In this paper, the two-dimensional Zakharov-Kuznetsov-Burgers (ZKB) equation is investigated. The basic set of fluid equations is reduced to ZKB equation. This equation is a two-dimensional analog of the wellknown Korteweg-de Vries-Burgers equation, and also is typical example of so-called dispersive equations which attract the considerable attention of both pure and applied mathematicians in the past decades. We obtain traveling wave solutions for two-dimensional Zakharov-Kuznetsov-Burgers equation by modified Kudryashov method which is a powerful method for obtaining exact solutions of integrable and nonintegrable nonlinear evolution equations. Graphical representation of obtained solutions is demonstrated.

Numerical modeling of the task of support tension near cleaning

“…and tangential contact stresses acting on the edges of layered half-planes. Their behavior and size in the vicinity of the mine is determined by the properties of the coal seam, its compliance [[3],[4],[5]]. on the elastic characteristics of the layers and the formation,  K can go to zero.…”