New Soliton Solutions of the Burgers Equation with Additional Time-dependent Variable Coefficient

Abstract

In this article, we use the functional variational method to solve the Burgers equation with an additional time-dependent variable coefficient. The main advantage of the proposed method over other methods is that it allows to obtain more new solutions of the equation. Among the solutions obtained, new soliton solutions should be noted, which are of great importance for revealing the internal mechanism of physical phenomena. Three-dimensional graphs of solutions are constructed using the mathematical program Matlab. For a better understanding of the physical properties of some of the resulting solutions, their graphical representations are shown. This method is effective for finding exact solutions to many other similar wave equations.