Integrability of the Two-Layer Spin System

Nugmanova, Gulgassyl; Myrzakul, Akbota

doi:10.7546/giq-20-2019-208-214

Cited by 3 publications

(2 citation statements)

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“…The Hirota system is used to describe many nonlinear phenomena. It is widely used in the field of study of optical fiber systems, in the mechanisms of physics, electrical communication and other engineering sciences [8,9].…”

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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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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“…The interest in them is justified by the fact that with their help many physical processes are described in optics, radiophysics, in the dynamics of continuous media, particle physics and other fields. The more famous among (2+1)-dimensional integrable equations are the nonlinear Schrodinger equation (NLSE), the Ishimori equation, the sine-Gorden equation, the Kadomtsev-Petviashvili equation, the Zakharov-Manakov equation, the Davy-Stewartson equation, M-I etc [8][9][10][11][12][13]. Theories of solving problems for twodimensional integrable equations are more complicated, since (2+1)-dimensional connected with systems of linear partial differential equations with variable coefficients.…”

Section: Introductionmentioning

confidence: 99%

Gauge Equivalence Between the Г-Spin System and (2+1)-Dimensional Two-Component Nonlinear Schrodinger Equation

Myrzakul¹,

Myrzakulova²

2020

OF THE NATIONAL ACADEMY OFSCIENCES OF THE REPUBLIC OF KAZAKHSTA

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Б а с р е д а к т о р ы ф.-м.ғ.д., проф., ҚР ҰҒА академигі Ғ.М. Мұтанов Р е д а к ц и я а л қ а с ы: Жұмаділдаев А.С. проф., академик (Қазақстан) Кальменов Т.Ш. проф., академик (Қазақстан) Жантаев Ж.Ш. проф., корр.-мүшесі (Қазақстан) Өмірбаев У.У. проф., корр.-мүшесі (Қазақстан) Жүсіпов М.А. проф. (Қазақстан) Жұмабаев Д.С. проф. (Қазақстан) Асанова А.Т. проф. (Қазақстан) Бошкаев К.А. PhD докторы (Қазақстан) Сұраған Д. корр.-мүшесі (Қазақстан) Quevedo Hernando проф. (Мексика), Джунушалиев В.Д. проф. (Қырғыстан) Вишневский И.Н. проф., академик (Украина) Ковалев А.М. проф., академик (Украина) Михалевич А.А. проф., академик (Белорусь) Пашаев А. проф., академик (Әзірбайжан) Такибаев Н.Ж. проф., академик (Қазақстан), бас ред. орынбасары Тигиняну И. проф., академик (Молдова) «ҚР ҰҒА Хабарлары. Физика-математикалық сериясы».

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Integrable Kuralay Equations: Geometry, Solutions and Generalizations

et al. 2022

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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. Some integrable generalizations and other related nonlinear differential equations are presented.

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Integrability of the Two-Layer Spin System

Cited by 3 publications

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

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

Gauge Equivalence Between the Г-Spin System and (2+1)-Dimensional Two-Component Nonlinear Schrodinger Equation

Integrable Kuralay Equations: Geometry, Solutions and Generalizations

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