Lie symmetry based-analytical and numerical approach for modified Burgers-KdV equation

Abstract

In this work, the variable-coefficient modified Burgers-KdV equation, which arises in modeling various physical phenomena, is studied for exact and numerical solution based on Lie symmetry. The infinitesimals of the group of transformations which leaves this equation invariant are furnished along with the admissible forms of the variable coefficients. The optimal systems of one-dimensional subalgebras of the Lie symmetry algebras are determined with the adjoint action of the symmetry group. These are then used to establish new power series solution and exact solutions of variable-coefficient modified Burgers-KdV equation. Further, RK4 (e.g. Fourth Order Runge Kutta) method is applied to the reduced ODE for constructing numerical solutions of the modified Burger-KdV equation. Keywords: Modified Burgers-KdV equations, Symmetry reductions, Exact solutions, Power series solutions, Numerical solutions