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

Yergaliyeva, Gulmira; Myrzakul, Tolkynay; Nugmanova, Gulgassyl; Myrzakulov, Ratbay

doi:10.7546/giq-21-2020-310-319

VOL. 21 | 2020 Camassa-Holm and Myrzakulov-CIV Equations with Self-Consistent Sources: Geometry and Peakon Solutions

Gulmira Yergaliyeva, Tolkynay Myrzakul, Gulgassyl Nugmanova, Ratbay Myrzakulov

Editor(s) Ivaïlo M. Mladenov, Vladimir Pulov, Akira Yoshioka

Geom. Integrability & Quantization, 2020: 310-319 (2020) DOI: 10.7546/giq-21-2020-310-319

Abstract

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.