Camassa-Holm and Myrzakulov-CIV Equations with Self-Consistent Sources: Geometry and Peakon Solutions

In this paper, we study one of generalized Heisenberg ferromagnet equations with self-consistent sources, namely, the so-called Myrzakulov-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 to each 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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