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Hamiltonian Structure, Symmetries and Conservation Laws for a Generalized (2 + 1)-Dimensional Double Dispersion Equation

Department of Mathematics, Universidad de Cádiz, Puerto Real, 11510 Cádiz, Spain
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Symmetry 2019, 11(8), 1031; https://doi.org/10.3390/sym11081031
Received: 15 July 2019 / Revised: 5 August 2019 / Accepted: 6 August 2019 / Published: 9 August 2019
(This article belongs to the Special Issue Noether's Theorem and Symmetry)
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Abstract

This paper considers a generalized double dispersion equation depending on a nonlinear function f ( u ) and four arbitrary parameters. This equation describes nonlinear dispersive waves in 2 + 1 dimensions and admits a Lagrangian formulation when it is expressed in terms of a potential variable. In this case, the associated Hamiltonian structure is obtained. We classify all of the Lie symmetries (point and contact) and present the corresponding symmetry transformation groups. Finally, we derive the conservation laws from those symmetries that are variational, and we discuss the physical meaning of the corresponding conserved quantities. View Full-Text
Keywords: Lie symmetry; conservation law; double dispersion equation; Boussinesq equation Lie symmetry; conservation law; double dispersion equation; Boussinesq equation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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MDPI and ACS Style

Recio, E.; Garrido, T.M.; de la Rosa, R.; Bruzón, M.S. Hamiltonian Structure, Symmetries and Conservation Laws for a Generalized (2 + 1)-Dimensional Double Dispersion Equation. Symmetry 2019, 11, 1031.

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