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integrability and Solutions of the (2+1)-Dimensional Broer-Kaup Equation with Variable Coefficients

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Communications in Theoretical Physics 2012年第9期58卷 387-392页

作者：王路华贺劲松 Department of Mathematics Ningbo University

The integrability of the （2＋l）-dimensional Broer-Kaup equation with variable coefficients （VCBK） is verified by finding a transformation mapping it to the usual （2＋l）-dimensional Broer-Kaup equation （BK）. Thus the solutions of the （2＋1）-dimensional VCBK are obtained by making full use of the known solutions of the usual （2＋1）dimensional IRK. Two new integrable models are given by this transformation, their dromion-like solutions and rogue wave solutions are also obtained. Further, the velocity of the dromion-like solutions can be designed and the center of the rogue wave solutions can be controlled artificially because of the appearance of the four arbitrary functions in the transformation.

关键词： (2+l)-dimensional Broer Kaup equation with variable coefficients integrability (2+1)-dimen-sional Broer-Kaup equation dromion-like rogue wave

integrability Condition on an Almost Complex Structure and Its Application

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Acta Mathematica Sinica,English Series 2005年第6期21卷 1459-1464页

作者： Chia Kuei PENG Zi Zhou TANG(Zizhou TANG) Department of Mathematics Graduate School The Chinese Academy of Sciences Beijing 100039 P. R. China School of Mathematical Sciences Beijing Normal University Beifing 100875 P. R. China Department of Mathematical Sciences Tsinghua University Beijing 100084 P. R. China

We obtain and apply a simple form of the integrability condition of an almost complex structure to the Hopf manifolds.

关键词： almost complex structure integrability

integrability and Gauge Fixing for Bosonic String on AdS_3×S^3

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Communications in Theoretical Physics 2008年第7期50卷 129-132页

作者： KE San-Min WANG Chun SHI Kang-Jie College of Science Chang＇an University Xi＇an 710064 China Institute of Modern Physics Northwest University Xi＇an 710069 China College of Science Xi＇an Shiyou University Xi＇an 710065 China

The integrability and the TST transformation of the bosonic string on AdS3× S^3 are studied. The Lax connection for gauge fixed theory is constructed and proved to be fiat.

关键词： integrability TST transformation Lax connection fiat

integrability of Nonlinear Equations of Motion on Two-Dimensional World Sheet Space-Time

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Communications in Theoretical Physics 2005年第2X期44卷 283-287页

作者： YAN Jun Department of Physics Sichuan Normal University Chengdu 610066 China

The integrability character of nonlinear equations of motion of two-dimensional gravity with dynamical torsion and bosonic string coupling is studied in this paper. The space-like and time-like first integrals of equa... 详细信息

关键词： two-dimensional gravity model string coupling integrability

Painlevé integrability of the supersymmetric Ito equation

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Chinese Physics B 2019年第9期28卷 83-86页

作者： Feng-Jie Cen Yan-Dan Zhao Shuang-Yun Fang Huan Meng Jun Yu Department of Physics Shaoxing University

A supersymmetric version of the Ito equation is proposed by extending the independent and dependent variables for the classic Ito *** investigate the integrability of the N = 1 supersymmetric Ito(sIto) equation, a singularity structure analysis for this system is carried *** a detailed analysis in two cases by using Kruskal’s simplified method, the sIto system is found to pass the Painlevé test, and thus is Painlevé integrable.

关键词： supersymmetric Ito equation Painlevé analysis integrability

Classical integrability of strings in γ-deformed backgrounds

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Chinese Physics B 2008年第11期17卷 4153-4157页

作者：解小宁岳瑞宏 SKLLQG Institute of Earth Environment Chinese Academy of Sciences Institute of Modern Physics Northwest University Department of Physics Ningbo University

This paper considers classical strings propagating in γ-deformed AdS3 γ S^3 backgrounds generated by certain shift T-dualities accompanied （TsT） transformations on S^3 and AdS3, respectively. It finds that the U（1） currents of strings with the twisted boundary conditions are equal to those in γ-deformed backgrounds generated by TsT transformations on both S3 and ADS3. Applying the TsT transformations, it derives the local Lax connections and the monodromy matrices in γ-deformed backgrounds with the spectral parameter which ensure the classical integrability of the string theories.

关键词： TsT transformation Lax connection monodromy matrix integrability

On the integrability of the Abel and of the Extended Liénard Equations

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Acta Mathematicae Applicatae Sinica 2019年第4期35卷 722-736页

作者： Man Kwong Mak Tiberiu HARKO Departamento de Fsica Facultad de Ciencias Naturales Universidad de Atacama Copayapu 485 Copiapo Chile Department of Physics Babes-Bolyai University Kogalniceanu Street Cluj-Napoca 400084 Romania School of Physics Sun Yat-Sen University Guangzhou 510275 China

We present some exact integrability cases of the extended Liénard equation y′′+ f(y)(y′)n +k(y)(y′)m + g(y)y′+ h(y) = 0, with n > 0 and m > 0 arbitrary constants, while f(y), k(y), g(y), and h(y) are arbitrary functions. The solutions are obtained by transforming the equation Liénard equation to an equivalent first kind first order Abel type equation given bydv/dy= f(y)v3-n+ k(y)v3-m+ g(y)v2+ h(y)v3, with v = 1/y′.As a first step in our study we obtain three integrability cases of the extended quadratic-cubic Liénard equation,corresponding to n = 2 and m = 3, by assuming that particular solutions of the associated Abel equation are known. Under this assumption the general solutions of the Abel and Liénard equations with coefficients satisfying some differential conditions can be obtained in an exact closed form. With the use of the Chiellini integrability condition, we show that if a particular solution of the Abel equation is known, the general solution of the extended quadratic cubic Liénard equation can be obtained by quadratures. The Chiellini integrability condition is extended to generalized Abel equations with g(y) ≡ 0 and h(y) ≡ 0, and arbitrary n and m, thus allowing to obtain the general solution of the corresponding Liénard equation. The application of the generalized Chiellini condition to the case of the reduced Riccati equation is also considered.

关键词： Abel equation Liénard equation general solutions integrability conditions

Notes on index of quantum integrability

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Communications in Theoretical Physics 2021年第5期73卷 1-9页

作者： Jia Tian Jue Hou Bin Chen School of Physics and State Key Laboratory of Nuclear Physics and Technology Peking UniversityNo.5 Yiheyuan RdBeijing 100871China Center for High Energy Physics Peking UniversityNo.5 Yiheyuan RdBeijing 100871China Collaborative Innovation Center of Quantum Matter No.5 Yiheyuan RdBeijing 100871China

A quantum integrability index was proposed in Komatsu et al(2019 SciPost Phys.7065).It systematizes the Goldschmidt and Witten's operator counting argument(Goldschmidt and Witten 1980 ***.B 91392)by using the conformal *** this work we compute the quantum integrability indexes for the symmetric coset models SU(N)/SO(N)and SO(2N)/SO(N)×SO(N).The indexes of these theories are all non-positive except for the case of SO(4)/SO(2)×SO(2).Moreover we extend the analysis to the theories with fermions and consider a concrete theory:the CP~N model coupled with a massless Dirac *** find that the indexes for this class of models are non-positive as well.

关键词： integrability quantum index coset models

On the integrability of Strictly Convex Billiard Tables with Boundaries Close to Ellipses with Small Eccentricities

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Acta Mathematica Sinica,English Series 2022年第1期38卷 55-67页

作者： Guan HUANG Yau Mathematical Sciences Center Tsinghua UniversityBeijing 100084P.R.China

In this paper,we introduce a new notion of integrability for billiard tables,namely,integrability away from the *** key feature of our notion is that the integrable region could be disjoint from the boundary with a positive *** prove that if a strictly convex billiard table,whose boundary is a small perturbation of an ellipse with small eccentricity,is integrable in this sense,then its boundary must be itself an ellipse.

关键词： Birkhoff conjecture Billiard tables integrability