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Symmetry
Volume 11
Issue 8
10.3390/sym11081031
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Article

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

by
Elena Recio
*,
Tamara M. Garrido
,
Rafael de la Rosa
and
María S. Bruzón
Department of Mathematics, Universidad de Cádiz, Puerto Real, 11510 Cádiz, Spain
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(8), 1031; https://doi.org/10.3390/sym11081031
Submission 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)
Versions Notes

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.
Keywords: Lie symmetry; conservation law; double dispersion equation; Boussinesq equation Lie symmetry; conservation law; double dispersion equation; Boussinesq equation

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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. https://doi.org/10.3390/sym11081031

AMA Style

Recio E, Garrido TM, de la Rosa R, Bruzón MS. Hamiltonian Structure, Symmetries and Conservation Laws for a Generalized (2 + 1)-Dimensional Double Dispersion Equation. Symmetry. 2019; 11(8):1031. https://doi.org/10.3390/sym11081031

Chicago/Turabian Style

Recio, Elena, Tamara M. Garrido, Rafael de la Rosa, and María S. Bruzón. 2019. "Hamiltonian Structure, Symmetries and Conservation Laws for a Generalized (2 + 1)-Dimensional Double Dispersion Equation" Symmetry 11, no. 8: 1031. https://doi.org/10.3390/sym11081031

APA Style

Recio, E., Garrido, T. M., de la Rosa, R., & Bruzón, M. S. (2019). Hamiltonian Structure, Symmetries and Conservation Laws for a Generalized (2 + 1)-Dimensional Double Dispersion Equation. Symmetry, 11(8), 1031. https://doi.org/10.3390/sym11081031

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