%0 Journal Article 
%A Bruzón Gallego, María de los Santos
%A Rosa Silva, Rafael de la
%A Gandarias Núñez, María Luz
%A Tracinà, Rita
%T Reductions and Conservation Laws of a Generalized Third-Order PDE via Multi-Reduction Method
%D 2022
%@ 2227-7390
%U http://hdl.handle.net/10498/26725
%X 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 of this type
model several real-world phenomena, such as diffusion, convection, or dispersion processes, only to
cite a few. By using the multiplier method, we compute conservation laws. Looking for traveling
waves solutions, all the the conservation laws that are invariant under translation symmetries are
directly obtained. Moreover, each of them will be inherited by the corresponding traveling wave
ODEs, and a set of first integrals are obtained, allowing to reduce the nonlinear third-order evolution
equations under consideration into a first-order autonomous equation.
%K third-order partial differential equations
%K conservation laws
%K multi-reduction method
%K partial differential equations
%~ Universidad de Cádiz