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

María S. Bruzón, Rafael de la Rosa, María L. Gandarias and Rita Tracinà
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María S. Bruzón: Departamento de Matemáticas, Universidad de Cádiz, 11510 Puerto Real, Spain
Rafael de la Rosa: Departamento de Matemáticas, Universidad de Cádiz, 11510 Puerto Real, Spain
María L. Gandarias: Departamento de Matemáticas, Universidad de Cádiz, 11510 Puerto Real, Spain
Rita Tracinà: Dipartimento di Matematica e Informatica, Università di Catania, 95125 Catania, Italy

Mathematics, 2022, vol. 10, issue 6, 1-13

Abstract: 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.

Keywords: third-order partial differential equations; conservation laws; multi-reduction method; partial differential equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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