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Article

Lie Symmetries and Low-Order Conservation Laws of a Family of Zakharov-Kuznetsov Equations in 2 + 1 Dimensions

Department of Mathematics, Universidad de Cádiz, Puerto Real, 11510 Cádiz, Spain
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Symmetry 2020, 12(8), 1277; https://doi.org/10.3390/sym12081277
Received: 8 June 2020 / Revised: 10 July 2020 / Accepted: 14 July 2020 / Published: 2 August 2020
(This article belongs to the Special Issue Conservation Laws and Symmetries of Differential Equations)
In this work, we study a generalised (2+1) equation of the Zakharov–Kuznetsov (ZK)(m,n,k) equation involving three arbitrary functions. From the point of view of the Lie symmetry theory, we have derived all Lie symmetries of this equation depending on the arbitrary functions. Line soliton solutions have also been obtained. Moreover, we study the low-order conservation laws by applying the multiplier method. This family of equations is rich in Lie symmetries and conservation laws. Finally, when the equation is expressed in potential form, it admits a variational structure in the case when two of the arbitrary functions are linear. In addition, the corresponding Hamiltonian formulation is presented. View Full-Text
Keywords: ZK equations; Lie symmetries; conservation laws ZK equations; Lie symmetries; conservation laws
MDPI and ACS Style

Bruzón, M.S.; Garrido, T.M.; Recio, E.; de la Rosa, R. Lie Symmetries and Low-Order Conservation Laws of a Family of Zakharov-Kuznetsov Equations in 2 + 1 Dimensions. Symmetry 2020, 12, 1277. https://doi.org/10.3390/sym12081277

AMA Style

Bruzón MS, Garrido TM, Recio E, de la Rosa R. Lie Symmetries and Low-Order Conservation Laws of a Family of Zakharov-Kuznetsov Equations in 2 + 1 Dimensions. Symmetry. 2020; 12(8):1277. https://doi.org/10.3390/sym12081277

Chicago/Turabian Style

Bruzón, María S., Tamara M. Garrido, Elena Recio, and Rafael de la Rosa. 2020. "Lie Symmetries and Low-Order Conservation Laws of a Family of Zakharov-Kuznetsov Equations in 2 + 1 Dimensions" Symmetry 12, no. 8: 1277. https://doi.org/10.3390/sym12081277

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