Exact analytic, regular perturbation and numerical solutions of symmetry reductions of a (2+1) -dimensional KdV–Burgers equation

The (2+1)-dimensional generalized KdV–Burgers equation, (ut+unux+λ(x,y,t)uxx+α(x,y,t)uxxx)x+S(x,y,t)uyy=0(ut+unux+λ(x,y,t)uxx+α(x,y,t)uxxx)x+S(x,y,t)uyy=0, is changed to its canonical form via allowed transformations and then the canonical equation is subjected to Lie’s symmetry analysis. Exact and regular perturbation solutions are obtained for the reduced partial differential equations. Regular perturbation and numerical solutions are reported for the reduced second order nonlinear ordinary differential equations.