Reductions and Conservation Laws of a Generalized Third-Order PDE via Multi-Reduction Method

In this work, we consider a family of nonlinear third-order evolution equations, where two arbitrary functions depending on the dependent variable appear. Evolution equations type model several real-world phenomena, such as diffusion, convection, or dispersion processes, only to cite few. By using multiplier method, compute conservation laws. Looking for traveling waves solutions, all laws that are invariant under translation symmetries directly obtained. Moreover, each them will be inherited by corresponding wave ODEs, and set first integrals obtained, allowing reduce consideration into first-order autonomous equation.