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

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2019-08Department
MatemáticasSource
Symmetry 2019, 11(8)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.
Subjects
Lie symmetry; conservation law; double dispersion equation; Boussinesq equationCollections
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