Group method solutions of the generalized forms of Burgers, Burgers-KdV and KdV equations with time-dependent variable coefficients

Solutions for the generalized forms of Burgers, Burgers-KdV, and KdV equations with time-dependent variable coefficients and with initial and boundary conditions are constructed. The analysis rests mainly on the standard group method. Similarity solutions are found which reduce the nonlinear system of partial differential equations to systems of ordinary differential equations to obtain some exact solutions and others as numerical solutions.