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Generalizations of the finite nonperiodic Toda lattice and its Darboux transformation

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Communications in Theoretical Physics 2021年第8期73卷 18-30页

作者： Jian li chuanzhong li School of Mathematics and Statistics Ningbo UniversityNingbo315211China College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao266590China

In this paper,we construct Hamiltonian systems for 2 N particles whose force depends on the distances between the *** obtain the generalized finite nonperiodic Toda equations via a symmetric group *** solutions of the generalized Toda equations are derived using the tau *** relationship between the generalized nonperiodic Toda lattices and lie algebras is then be discussed and the generalized Kac-van Moerbeke hierarchy is split into generalized Toda lattices,whose integrability and Darboux transformation are studied.

关键词： Hamiltonian systems Toda lattices Darboux transformation lie algebra Kac-van Moerbeke hierarchy

On limit fractional Volterra hierarchies

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Communications in Theoretical Physics 2024年第1期76卷 7-16页

作者： lixiang Zhang chuanzhong li School of Mathematics and Statistics Ningbo UniversityNingbo315211China College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao266590China

For the limit fractional Volterra(LFV)hierarchy,we construct the n-fold Darboux transformation and the soliton ***,we extend the LFV hierarchy to the noncommutative LFV(NCLFV)hierarchy,and construct the Darboux transformation expressed by quasi determinant of the noncommutative ***,we establish the relationship between new and old solutions of the NCLFV ***,the quasi determinant solutions of the NCLFV hierarchy are obtained.

关键词： limit fractional Volterra hierarchy noncommutative limit fractional Volterra hierarchy Darboux transformation soliton solution quasi determinant solution

Regular Solution and Lattice Miura Transformation of Bigraded Toda Hierarchy

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Chinese Annals of Mathematics,Series B 2013年第6期34卷 865-884页

作者： chuanzhong li Jingsong HE Department of Mathematics Ningbo University

The authors give finite dimensional exponential solutions of the bigraded Toda hierarchy （BTH）. As a specific example of exponential solutions of the BTH, the authors consider a regular solution for the （1, 2）-BTH with a 3 × 3-sized Lax matrix, and discuss some geometric structures of the solution from which the difference between the （1, 2）- BTH and the original Toda hierarchy is shown. After this, the authors construct another kind of Lax representation of （N, 1）-BTH which does not use the fractional operator of Lax operator. Then the authors introduce the lattice Miura transformation of （N, 1）-BTH which leads to equations depending on one field, and meanwhile some specific examples which contain the Volterra lattice equation （a useful ecological competition model） are given.

关键词： Regular solution Lattice Miura transformation Bigraded Toda hierarchy Moment polytope Volterra lattice

Noncommutative Constrained KP Hierarchy and Multi-component Noncommutative Constrained KP Hierarchy

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Chinese Annals of Mathematics,Series B 2019年第3期40卷 457-468页

作者： Qiufang liU chuanzhong li Department of Mathematics Ningbo University

In this paper, the authors define the noncommutative constrained KadomtsevPetviashvili(KP) hierarchy and multi-component noncommutative constrained KP hierarchy. Then they give the recursion operators for the noncommutative constrained KP(NcKP) hierarchy and multi-component noncommutative constrained KP(NmcKP) hierarchy. The authors hope these studies might be useful in the study of D-brane dynamics whose noncommutative coordinates emerge from limits of the M theory and string theory.

关键词： Recursion operator Noncommutative constrained KP hierarchy Multi-component noncommutative constrained KP hierarchy

Darboux transformation and positons of the inhomogeneous Hirota and the Maxwell-Bloch equation

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Science China(Physics,Mechanics & Astronomy) 2014年第5期57卷 898-907页

作者： li chuanzhong HE JingSong Department of Mathematics Ningbo University

In this paper,we derive Darboux transformation of the inhomogeneous Hirota and the Maxwell-Bloch(IH-MB)equations which are governed by femtosecond pulse propagation through inhomogeneous doped *** determinant represen... 详细信息

关键词： inhomogeneous Hirota and Maxwell-Bloch equations Darboux transformation soliton solution positon solution

Quantum Torus lie Algebra in the q-Deformed Kadomtsev-Pe tv iashvili Sys tern

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Algebra Colloquium 2019年第4期26卷 579-588页

作者： chuanzhong li Xinyue li Fushan li Yucai Su School of Mathematics and Statistics Ningbo University NingboZhejiang 315211China College of Mathematics and Systems Science Shandong University of Science and Technology QingdaoShandong 266590China School of Mathematical Sciences Qufu Normal University QufuShandong 273165China 不详

Based on the symmetry of the Q-deformed Kadomtsev-Petviashvili(q-KP)hierarchy,which is a q-deformation of the KP hierarchy,we construct the quantum torus symmetry of the q-KP hierarchy,which further leads to the quantum torus constraint of its tau ***,we generalize the system to a multi-component q-KP hierarchy that also has the well-known ghost symmetry.

关键词： q-KP hierarchy Baker-Akhiezer function ghost symmetry quantum torus symmetry quantum torus constraint multi-component q-KP hierarchy

Research and Realization of Streaming Media Digital Rights Management

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Research and Realization of Streaming Media Digital Rights M...

Nonsingular Positon Solutions of a Variable-Coefficient Modified KdV Equation

2011 International Conference on Informatics,Cybernetics,and Computer Engineering(ICCE 2011)

作者： Jun Xie chuanzhong li College of Information Engineering Capital Normal University

Digital rights management（DRM） is becoming a key enabling technology to protect intellectual property of digital contents, control their dissemination and usage. Combining the actual application situation of the current stream license technology and the new generation of DRM technology, and then poses a concrete scheme for the digital right management system. What’s more, it realizes the streaming media digital rights management system finally according to the scheme.

关键词： DRM Streaming Media Digital Rights Management

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Open Journal of Applied Sciences 2013年第1期3卷 102-105页

作者： Yi lin chuanzhong li Jingsong He Department of Mathematics Ningbo University Ningbo China

The determinant representation of three-fold Darboux transformation for a variable-coefficient modified KdV equation is displayed based on the technique used to solve Ablowitz-Kaup-Newell-Segur system. Additionally, the nonsingular positon solutions of the variable-coefficient modified KdV equation are firstly discovered analytically and graphically.

关键词： Variable-Coefficient KdV Equation Lax Pair Darboux Transformation Positon Soliton-Positon

Rogue Waves of the Kundu-DNLS Equation

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Open Journal of Applied Sciences 2013年第1期3卷 99-101页

作者： Shibao Shan chuanzhong li Jingsong He Department of Mathematics Ningbo University Ningbo China

In this paper, we give the Lax pair and construct the Darboux transformation of the Kundu-DNLS equation. Furthermore, the rogue wave solutions of the Kundu-DNLS equation are derived by using the Taylor expansion of the breather solution. What's more, the triangular and the circular patterns of the third rouge solution are displayed.

关键词： Kundu-DNLS Equation Darboux Transformation Rogue Waves