Integrable motion of two interacting curves, spin systems and the Manakov system

Myrzakul, Akbota; Myrzakulov, Ratbay

doi:10.1142/s0219887817501158

Cited by 11 publications

(5 citation statements)

References 29 publications

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“…It is well known that in 1+1 and 2+1 dimensions there exists geometrical equivalence between spin systems and nonlinear Schrödinger type equations [4]- [35], which we called the Lakshmanan equivalence or shortly the L-equivalence. In this section we find the L-equivalent counterpart of the K-IIAE (2.1)-(2.3).…”

Section: Integrable Motion Of Space Curves Induced By the K-iiementioning

confidence: 99%

Integrable Kuralay equations: geometry, solutions and generalizations

Sagidullayeva¹,

Nugmanova²,

Myrzakulov³

et al. 2022

Preprint

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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 equations is established. With the help of the Hirota bilinear method, the simplest soliton solutions are also presented. The nonlocal and dispersionless versions of the Kuralay equations are considered.

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Section: Integrable Motion Of Space Curves Induced By the K-iiementioning

confidence: 99%

Integrable Kuralay equations: geometry, solutions and generalizations

Sagidullayeva¹,

Nugmanova²,

Myrzakulov³

et al. 2022

Preprint

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“…There are several ways to obtain nonlinear soliton solutions of evolutionary equations. These include the nonlinear method of the Hirota equation, the Darboux transformation (DT), the Painleve analysis, and more [1][2][3][4][5][6][7].…”

Section: Thematic Scope: Publication Of Priority Research In the Field Of Physical And Mathematical Sciences And Information Technologymentioning

confidence: 99%

Multi-Line Soliton Solutions for the Two-Dimensional Nonlinear Hirota Equation

Bekova

Жадыранова

2021

News of NAN RK. SGTS

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At present, the question of studying multidimensional nonlinear integrable equations in the framework of the theory of solitons is very interesting to foreign and Kazakh scientists. Many physical phenomena that occur in nature can be described by nonlinearly integrated equations. Finding specific solutions to such equations plays an important role in studying the dynamics of phenomena occurring in various scientific and engineering fields, such as solid state physics, fluid mechanics, plasma physics and nonlinear optics. There are several methods for obtaining real and soliton, soliton-like solutions of such equations: the inverse scattering method, the Hirota’s bilinear method, Darboux transformation methods, the tanh-coth and the sine-cosine methods. In our work, we studied the two-dimensional Hirota equation, which is a modified nonlinear Schrödinger equation. The nonlinear Hirota equation is one of the integrating equations and the Hirota system is used in the field of study of optical fiber systems, physics, telecommunications and other engineering fields to describe many nonlinear phenomena. To date, the first, second, and n-order Darboux transformations have been developed for the two- dimensional system of Hirota equations, and the soliton, rogue wave solutions have been determined by various methods. In this article, we consider the two-dimensional nonlinear Hirota equations. Using the Lax pair and Darboux transformation we obtained the first and the second multi-line soliton solutions for this equation and provided graphical representation.

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“…Подставим (16), (17), (18) в (9) и получим первую фундаментальную форму для уравнения Камасса-Холма:…”

Section: первая фундаментальная форма поверхности для уравнения камасunclassified