TL;DR
This paper introduces a double extended two-component Novikov equation with a bi-Hamiltonian structure, expanding the class of peakon equations and their integrable properties.
Contribution
It presents a novel double extended two-peakon Novikov equation with a bi-Hamiltonian structure, generalizing previous peakon models.
Findings
Derived the Hamiltonian structure for the supersymmetric N=2 Novikov equation.
Formulated the two-component generalization of the cubic peakon equation.
Constructed the bi-Hamiltonian structure for the extended system.
Abstract
The Hamiltonian structure for the supersymmetric Novikov equation is presented. The bosonic sector give us two-component generalization of the cubic peakon equation. The double extended: two-component and two-peakon Novikov equation is defined. The Bi-Hamiltonian structure for this extended system is constructed.
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