Integrable Kuralay Equations: Geometry, Solutions and Generalizations

Autor: Zhanna Sagidullayeva, Gulgassyl Nugmanova, Ratbay Myrzakulov, Nurzhan Serikbayev

Publikováno v: Symmetry, Vol 14, Iss 7, p 1374 (2022)

In this paper, we study the Kuralay equations, namely the Kuralay-I equation (K-IE) and the Kuralay-II equation (K-IIE). The integrable motion of space curves induced by these equations is investigated. The gauge equivalence between these two equatio

Externí odkaz: https://doaj.org/article/1bb9da70e4ed403ba2d3354d3a00eaa2

Integrable (2 + 1)-Dimensional Spin Models with Self-Consistent Potentials

Autor: Ratbay Myrzakulov, Galya Mamyrbekova, Gulgassyl Nugmanova, Muthusamy Lakshmanan

Publikováno v: Symmetry, Vol 7, Iss 3, Pp 1352-1375 (2015)

Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schrödinger family of equations. In thi

Externí odkaz: https://doaj.org/article/dff654cb679144bcb724bbe818900e73

Integrable Tolkynay equations and related Yajima-Oikawa type equations

Autor: Zhaidary Myrzakulova, Gulgassyl Nugmanova, Yesmakhanova, Kuralay, Serikbayev, Nurzhan, Ratbay Myrzakulov

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::615df54e4a92b014720caa121e94f0e4

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

Autor: Tolkynay Myrzakul, Gulgassyl Nugmanova, Ratbay Myrzakulov, Gulmira Yergaliyeva

Publikováno v: Proceedings of the Twenty-First International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Vladimir Pulov and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2020)

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

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4b047069531c24586303e995ca3f6291
https://projecteuclid.org/euclid.pgiq/1602640846

Integrability of the Two-Layer Spin System

Autor: Gulgassyl Nugmanova, Akbota Myrzakul

Publikováno v: Proceedings of the Twentieth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Vladimir Pulov and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2019)

Among nonlinear evolutionary equations integrable ones are of particular interest since only in this we case can theoretically study the model in detail and in-depth. In the present, we establish the geometric connection of the well-known integrable

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::16fb619340112bdacfe473f6dd0d8028
https://projecteuclid.org/euclid.pgiq/1545361494