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Register a new userDouble Extended Cubic Peakon Equation
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Ziemowit Popowicz ziemek
Publication date
2014
fields
Physics
and research's language is
English
Authors
Ziemowit Popowicz
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The Hamiltonian structure for the supersymmetric $N=2$ 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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In this paper, we propose a finite Toda lattice of CKP type (C-Toda) together with a Lax pair. Our motivation is based on the fact that the Camassa-Holm (CH) peakon dynamical system and the finite Toda lattice may be regarded as opposite flows in some sense. As an intriguing analogue to the CH equation, the Degasperis-Procesi (DP) equation also supports the presence of peakon solutions. Noticing that the peakon solution to the DP equation is expressed in terms of bimoment determinants related to the Cauchy kernel, we impose opposite time evolution on the moments and derive the corresponding bilinear equation. The corresponding quartic representation is shown to be a continuum limit of a discrete CKP equation, due to which we call the obtained equation finite Toda lattice of CKP type. Then, a nonlinear version of the C-Toda lattice together with a Lax pair is derived. As a result, it is shown that the DP peakon lattice and the finite C-Toda lattice form opposite flows under certain transformation.
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In this paper, we study one of generalized Heisenberg ferromagnet equations with self-consistent sources, namely, the so-called M-CIV equation with self-consistent sources (M-CIVESCS). The Lax representation of the M-CIVESCS is presented. We have shown that the M-CIVESCS and the CH equation with self-consistent sources (CHESCS) is geometrically equivalent each to other. The gauge equivalence between these equations is proved. Soliton (peakon) and pseudo-spherical surfaces induced by these equations are considered. The one peakon solution of the M-CIVESCS is presented.
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