关于两类多分量海森堡铁磁链模型的研究

数学物理学报 ›› 2022, Vol. 42 ›› Issue (5): 1348-1359.

关于两类多分量海森堡铁磁链模型的研究

王菲¹(),李登慧¹(),加羊杰²(),颜昭雯^1,*()

¹ 内蒙古大学数学科学学院呼和浩特 010021
² 青海师范大学民族师范学院数学系西宁 810008

收稿日期:2021-06-28 出版日期:2022-10-26 发布日期:2022-09-30
通讯作者: 颜昭雯 E-mail:neida_wangfei1@163.com;18443199972@163.com;jiayangjie123@163.com;yanzw@imu.edu.cn
作者简介:王菲, E-mail: neida_wangfei1@163.com|李登慧, E-mail: 18443199972@163.com|加羊杰, E-mail: jiayangjie123@163.com
基金资助:
国家自然科学基金(11965014);国家自然科学基金(12061051);青海省国家科学基金(2021-ZJ-708)

Two Types of Multi-Component Heisenberg Ferromagnet Models

Fei Wang¹(),Denghui Li¹(),Yangjie Jia²(),Zhaowen Yan^1,*()

¹ School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021
² Department of Mathematics, Nationalities College of Qinghai Normal University, Xining 810008

Received:2021-06-28 Online:2022-10-26 Published:2022-09-30
Contact: Zhaowen Yan E-mail:neida_wangfei1@163.com;18443199972@163.com;jiayangjie123@163.com;yanzw@imu.edu.cn
Supported by:
the NSFC(11965014);the NSFC(12061051);the NSF of Qinghai(2021-ZJ-708)

摘要/Abstract

摘要：

该文研究了两类多分量海森堡铁磁链模型, 分别为(1+1) 维Myrzakulov系列方程和(2+1) 维Myrzakulov Lakshmanan系列方程. 利用欧氏空间中曲线的运动规律, 可以构造与这两类方程相对应的几何等价方程, 进一步得到了这两类多分量海森堡铁磁链模型的Lax表示.

关键词: 海森堡铁磁链模型, 多分量推广, 几何等价方程, Lax表示

Abstract:

This paper is concerned with two kinds of multi-component Heisenberg ferromagnet models. They are the (1+1)-dimensional Myrzakulov series equations and the (2+1)-dimensional Myrzakulov Lakshmanan series equations. Moving the space curve in Euclidean space presents the corresponding geometrical equivalent equations. Meanwhile the Lax representations of two types of multi-component Heisenberg ferromagnet models are investigated.

Key words: Heisenberg ferromagnet models, Multi-component models, Gauge equivalent equation, Lax representations

中图分类号:

王菲,李登慧,加羊杰,颜昭雯. 关于两类多分量海森堡铁磁链模型的研究[J]. 数学物理学报, 2022, 42(5): 1348-1359.

Fei Wang,Denghui Li,Yangjie Jia,Zhaowen Yan. Two Types of Multi-Component Heisenberg Ferromagnet Models[J]. Acta mathematica scientia,Series A, 2022, 42(5): 1348-1359.

参考文献 20

1	Lakshmanan M . Continuum spin system as an exactly solvable dynamical system. Phys Lett A, 1977, 61, 53- 54 doi: 10.1016/0375-9601(77)90262-6
2	Porsezian K , Lakshmanan M , Tamizhmani K M . Geometrical equivalence of a deformed Heisenberg spin equation and the generalized nonlinear Schrödinger equation. Phys Lett A, 1987, 124, 159- 160 doi: 10.1016/0375-9601(87)90243-X
3	Sym A , Wesselius W . Geodesic congruences and inhomogeneous Heisenberg ferromagnet. Phys Lett A, 1987, 120, 183- 186 doi: 10.1016/0375-9601(87)90332-X
4	Sun H , Shan W R , Tao B , Wang M , Tan Z . Analytic studies on a generalized inhomogeneous higher-order nonlinear Schrödinger equation for the Heisenberg ferromagnetic spin chain. Commun Nonlinear SCI, 2015, 20, 711- 718 doi: 10.1016/j.cnsns.2014.06.049
5	Myrzakulov R. On Some Integrable and Nonintegrable Soliton Equations of Magnets I-IV. Alma-Ata: HEPI, 1987
6	Gao B , Jiang N N , Cui J F , Yan Z W . The extended Z_n-Heisenberg ferromagnet model. Mod Phys Lett B, 2019, 33, 1950381
7	Konopelchenko B G , Matkarimov B T . On the inverse scattering transform for the Ishimori equation. Phys Lett A, 1989, 135, 183- 189 doi: 10.1016/0375-9601(89)90259-4
8	Myrzakulov R , Nugmanova G N , Syzdykova R N . Guage equivalence between (2+1)-dimensional continuous Heisenberg ferromagnetic models and nonlinear Schrödinger-type equations. J Phys A, 1999, 31, 9535- 9545
9	Esmakhanova K R, Nugmanova G N, Zhao W Z, Wu K. Integrable inhomogeneous Lakshmanan-Myrzakulov equation. 2006, arXiv: nlin/0604034
10	Daems E , Kuijlaars A B J . Multiple orthogonal polynomials of mixed type and non-intersecting Brownian motions. J Approx Theory, 2005, 146, 91- 114
11	Zhou P X . The Riemann-Hilbert problem and inverse scattering. Siam J Math Anal, 1989, 20, 966- 986 doi: 10.1137/0520065
12	Satsuma J . A Wronskian representation of n-solition solutions of nonlinear evolution equations. J Phys Soc Jpn, 1979, 46, 359- 360 doi: 10.1143/JPSJ.46.359
13	Kac V G , van de Leur J W . The n-component KP hierarchy and representation theory. J Math Phys, 2003, 44, 3245- 3293 doi: 10.1063/1.1590055
14	Hirota R . Discrete analogue of a generalized Toda equation. J Phys Soc Jpn, 1981, 50, 3785- 3791 doi: 10.1143/JPSJ.50.3785
15	Li C Z . Strongly coupled B-type universal characters and hierarchies. Theor Math Phys, 2019, 201, 1732- 1741 doi: 10.1134/S0040577919120067
16	Ma W X , Batwa S . A binary Darboux transformation for multicomponent NLS equations and their reductions. Anal Math Phys, 2021, 11, 1- 12 doi: 10.1007/s13324-020-00437-5
17	Sun H C , Han R , Yan Z W . Novel extended Z_n-Heisenberg ferromagnet models. Int J Geom Methods M, 2021, 18, 2150080
18	Myrzakulov R , Mamyrbekova G , Nugmanova G , Lakshmanan M . Integrable (2+1)-dimensional spin models with self-consistent potentials. Symmetry-Basal, 2013, 7, 1352- 1375
19	Ma W X . N-soliton solutions and the Hirota conditions in (1+1)-dimensions. Int J Nonlinear SCI Numer Simul, 2021, 22, 1- 10 doi: 10.1515/ijnsns-2019-0007
20	Ma W X . N-soliton solution of a combined pKP-BKP equation. J Geom Phys, 2021, 165, 104191 doi: 10.1016/j.geomphys.2021.104191

[1]	曾云波. 带附加项的AKNS方程族的Darboux变换[J]. 数学物理学报, 1995, 15(3): 337-345.
[2]	马文秀. 具有Lenard递推结构之发展方程族的Lax表示[J]. 数学物理学报, 1994, 14(4): 409-418.