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Dark Parameterizations,Equivalent Partner Fields and integrable systems

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Communications in Theoretical Physics 2011年第5期55卷 743-746页

作者： LOU Sen-Yue Faculty of Science Ningbo University Ningbo 315211 China Department of Physics Shanghai Jiao Tong University Shanghai 200240 China School of Mathematics Fudan University Shanghai 200433 China

After introducing dark parameters into the traditional physical models, some types of new phenomena may be found. An important difficult problem is how to directly observe this kind of physical phenomena. An alternative treatment is to introduce equivalent multiple partner fields. If use this ideal to integrable systems, one may obtain infinitely many new coupled integrable systems constituted by the original usuM field and partner fields. The idea is illustrated via the celebrate KdV equation. From the procedure, some byproducts can be obtained： A new method to find exact solutions of some types of coupled nonlinear physical problems, say, the perturbation KdV systems, is provided; Some new localized modes such as the staggered modes can be found and some new interaction phenomena like the ghost interaction are discovered.

关键词： dark X dark parameterization integrable systems exact solution

Exact surface energy and elementary excitations of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields

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Chinese Physics B 2023年第1期32卷 483-492页

作者：董家生路鹏程孙佩乔艺曹俊鹏郝昆杨文力 Institute of Modern Physics Northwest UniversityXi'an 710127China Beijing National Laboratory for Condensed Matter Physics Institute of PhysicsChinese Academy of SciencesBeijing 100190China School of Physics Northwest UniversityXi'an 710127China Peng Huanwu Center for Fundamental Theory Xi'an 710127China Shaanxi Key Laboratory for Theoretical Physics Frontiers Xi'an 710127China School of Physical Sciences University of Chinese Academy of SciencesBeijing 100049China Songshan Lake Materials Laboratory Dongguan 523808China

We study the physical properties of the XXX spin-1/2 chain with arbitrary non-diagonal boundary fields. By using a combination of numerical analysis and analytical method, we obtain the surface energy and elementary excitations of the model. It shows that the contributions of the two boundary fields to the surface energy are additive. We also find that there exists a kind of excitations related to the boundary string.

关键词： quantum spin chain integrable systems Bethe ansatz

Deformed integrable models from holomorphic Chern-Simons theory

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Science China(Physics,Mechanics & Astronomy) 2022年第10期65卷 53-74页

作者： Yi-Jun He Jia Tian Bin Chen School of Physics Peking UniversityBeijing 100871China Collaborative Innovation Center of Quantum Matter Beijing 100871China Center for High Energy Physics Peking UniversityBeijing 100871China Kavli Institute for Theoretical Sciences(KITS) University of Chinese Academy of SciencesBeijing 100190China

We study the approaches to two-dimensional integrable field theories via a six-dimensional(6 D) holomorphic Chern-Simons theory defined on twistor space. Under symmetry reduction, it reduces to a 4 D Chern-Simons theory, while under solving along fibres it leads to a four-dimensional(4 D) integrable theory, the anti-self-dual Yang-Mills or its generalizations. From both 4 D theories, various two-dimensional integrable field theories can be obtained. In this work, we try to investigate several twodimensional integrable deformations in this framework. We find that the λ-deformation, the rational η-deformation, and the generalized λ-deformation can not be realized from the 4 D integrable model approach, even though they could be obtained from the 4 D Chern-Simons theory. The obstacle stems from the incompatibility between the symmetry reduction and the boundary conditions. Nevertheless, we show that a coupled theory of the λ-deformation and the η-deformation in the trigonometric description could be obtained from the 6 D theory in both ways, by considering the case that(3, 0)-form in the 6 D theory is allowed to have zeros.

关键词： integrable systems gauge field theories classical field theories

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Notes on integrable boundary interactions of open SU(4) alternating spin chains

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Science China(Physics,Mechanics & Astronomy) 2018年第7期61卷 32-37页

作者： JunBao WH Department of Physics Tianjin University Tianjin 300350 China Center for High Energy Physics Peking University Beijing 100871 China

Ref. [J. High Energy Phys. 1708, 001(2017)] showed that the planar flavored Ahanory-Bergman-Jafferis-Maldacena(ABJM)theory is integrable in the scalar sector at two-loop order using coordinate Bethe ansatz. A salient feature of this case is that the boundary reflection matrices are anti-diagonal with respect to the chosen basis. In this paper, we relax the coefficients of the boundary terms to be general constants to search for integrable systems among this class. We found that the only integrable boundary interaction at each end of the spin chain aside from the one in ref. [J. High Energy Phys. 1708, 001(2017)] is the one with vanishing boundary interactions leading to diagonal reflection matrices. We also construct non-supersymmetric planar flavored ABJM theory which leads to trivial boundary interactions at both ends of the open chain from the two-loop anomalous dimension matrix in the scalar sector.

关键词： Chern-Simons gauge theory integrable systems expansions for large numbers of components

Double Wronskian Soliton Solution for Mixed AKNS System

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Chinese Physics Letters 2005年第12期22卷 2987-2990页

作者：郝宏海吕丽丽陈登远 Department of Mathematics Shanghai University Shanghai 200444

The Lax pair of the mixed Ablowitz-Kap-Newell-Segur （AKNS） system is obtained from compatibility condition. Hirota＇s bilinear form is derived by some dependent variable transformation. Moreover, by means of the Wronskian technique, the double Wronskian form of soliton solutions are found. Specially, the two-soliton solution is presented.

关键词： integrable systems KORTEWEG-DEVRIES WAVE EQUATIONS

Quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal characters

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Chinese Physics B 2022年第8期31卷 197-206页

作者： Denghui Li Fei Wang Zhaowen Yan School of Mathematical Sciences Inner Mongolia UniversityHohhot 010021China

This paper is concerned with construction of quantum fields presentation and generating functions of symplectic Schur functions and symplectic universal *** boson-fermion correspondence for these symmetric functions have been *** virtue of quantum fields,we derive a series of infinite order nonlinear integrable equations,namely,universal character hierarchy,symplectic KP hierarchy and symplectic universal character hierarchy,*** addition,the solutions of these integrable systems have been discussed.

关键词： quantum fields generating functions integrable systems symmetric functions boson–fermion correspondence

Multi-place physics and multi-place nonlocal systems

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Communications in Theoretical Physics 2020年第5期72卷 120-132页

作者： S Y Lou School of Physical Science and Technology Ningbo UniversityNingbo315211China

Multi-place nonlocal systems have attracted attention from many *** this paper,we mainly review the recent progresses on two-place nonlocal systems(Alice-Bob systems)and four-place nonlocal ***-place systems can firstly be derived from many physical problems by using a multiple scaling method with a discrete symmetry group including parity,time reversal,charge conjugates,rotations,field reversal and exchange *** nonlocal systems can also be derived from the symmetry reductions of coupled nonlinear systems via discrete symmetry *** the other hand,to solve multi-place nonlocal systems,one can use the symmetry-antisymmetry separation approach related to a suitable discrete symmetry group,such that the separated systems are coupled local *** using the separation method,all the known powerful methods used in local systems can be applied to nonlocal *** this review article,we take two-place and four-place nonlocal nonlinear Schr?dinger(NLS)systems and Kadomtsev-Petviashvili(KP)equations as simple examples to explain how to derive and solve *** types of novel physical and mathematical points related to the nonlocal systems are especially emphasized.

关键词： multi-place physics multi-place nonlocal systems symmetries integrable systems parity and time reversal soliton theory classical prohibitions

Localization of Nonlocal Symmetries and Symmetry Reductions of Burgers Equation

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Communications in Theoretical Physics 2017年第5期67卷 467-472页

作者：吴剑文楼森岳俞军 Center for Nonlinear Science and Department of Physics Ningbo University Institute of Nonlinear Science Shaoxing University

The nonlocal symmetries of the Burgers equation are explicitly given by the truncated Painlevé *** auto-B?cklund transformation and group invariant solutions are obtained via the localization procedure for the nonlocal residual symmetries. Furthermore, the interaction solutions of the solition-Kummer waves and the solition-Airy waves are obtained.

关键词： integrable systems Burgers equation nonlocal symmetries interactions among different waves

From decoupled integrable models to coupled ones via a deformation algorithm

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Communications in Theoretical Physics 2023年第10期75卷 38-44页

作者：杜文鼎孔德兴楼森岳 Zhejiang Qiushi Institute for Mathematical Medicine Hangzhou 311121China School of Physical Science and Technology Ningbo UniversityNingbo315211China

By using a reconstruction procedure of conservation laws of different models,the deformation algorithm proposed by Lou,Hao and Jia has been used to a new application such that a decoupled system becomes a coupled *** the new application to some decoupled systems such as the decoupled dispersionless Korteweg–de Vries(Kd V)systems related to dispersionless waves,the decoupled KdV systems related to dispersion waves,the decoupled KdV and Burgers systems related to the linear dispersion and diffusion effects,and the decoupled KdV and Harry–Dym(HD)systems related to the linear and nonlinear dispersion effects,we have obtained various new types of higher dimensional integrable coupled *** new models can be used to describe the interactions among different nonlinear waves and/or different effects including the dispersionless waves(dispersionless KdV waves),the linear dispersion waves(KdV waves),the nonlinear dispersion waves(HD waves)and the diffusion *** method can be applied to couple all different separated integrable models.

关键词： integrable systems deformation algorithm KdV equations higher dimensional integrable systems coupled and decoupled systems