Symmetries, Reductions and Different Types of Travelling Wave Solutions for Symmetric Coupled Burgers Equations

In this paper, the symmetry group method is used to obtain similarity reductions for generalized symmetric coupled Burgers-type equations. Two different cases for similarity reductions yield, therefore two different ordinary differential equations are solved. Many new different traveling wave solutions in the form of rational wave solutions, kink soliton, and periodic wave solutions are given with their Illustration graphics. The obtained solutions are novel and cover other obtained solutions in the literature. Finally, some graphs for the obtained shock and kink wave solutions will given to illustrate the wave propagation behavior.