Soliton solutions to the time-dependent coupled KdV–Burgers’ equation

In this article, the authors apply the Lie symmetry approach and the modified $( G'/G )$-expansion method for seeking the solutions of time-dependent coupled KdV–Burgers equation. Using suitable similarity transformations, the time-dependent coupled KdV–Burgers equation is reduced to a system of nonlinear ordinary differential equations. Further, the reduced system of nonlinear ordinary differential equations for the coupled KdV equation is solved with the help of the modified $( G'/G )$-expansion method to obtain soliton solutions which are expressed by hyperbolic functions, trigonometric functions, and rational functions.