The Investigation of Exact Solutions and Conservation Laws of the Classical Boussinesq System Via the Lie Symmetry Method
In this paper, by applying the lie symmetry method with the aid of Maple, we study the classical Boussinesq (CB) system to investigate some new exact solutions. Using the infinitesimal generators and the linear combinations of the vector fields to convert the system to ordinary differential equations (ODEs) with a new dependent variable. Also, using the infinitesimal generators we can obtain the adjoint table and the commutator table of lie algebra. We employ the generalized tanh-function method to solve the ODEs. Hence, we obtain various travelling wave solutions for the CB system. We can investigate these solutions by using figures. Additionally, conservation laws for the CB system are obtained.