Camassa-Holm and M-CIV equations with self-consistent sources: geometry and peakon solutions

Gulgassyl Nugmanova; Gulmira Yergaliyeva; Kuralay Yesmakhanova; Ratbay Myrzakulov; Tolkynay Myrzakul

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Camassa-Holm and M-CIV equations with self-consistent sources: geometry and peakon solutions

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arxiv 1909.10606 v1 pith:2O6X7TF2 submitted 2019-09-23 nlin.SI

Gulmira Yergaliyeva , Tolkynay Myrzakul , Gulgassyl Nugmanova , Kuralay Yesmakhanova , Ratbay Myrzakulov This is my paper · ORCID

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keywords equationsm-civescsself-consistentsourcespeakonequationm-civpresented

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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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