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arXiv · 1909.10606

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

Gulmira Yergaliyeva·Tolkynay Myrzakul·Gulgassyl Nugmanova·Kuralay Yesmakhanova·Ratbay Myrzakulov
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Abstract

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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Gulmira Yergaliyeva, Tolkynay Myrzakul, Gulgassyl Nugmanova, Kuralay Yesmakhanova, Ratbay Myrzakulov. 2019-09-23. Camassa-Holm and M-CIV equations with self-consistent sources: geometry and peakon solutions. https://arxiv.org/abs/1909.10606

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