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Binary Nonlinearization of the Nonlinear Schr?dinger Equation Under an Implicit Symmetry Constraint

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Acta Mathematicae Applicatae Sinica 2014年第2期30卷 379-388页

作者： jing YU jing-song he Yi CheNG School of Science Hangzhou Dianzi University Department of Mathematics University of Science and Technology of China School of Science Ningbo University

By modifying the procedure of binary nonlinearization for the AKNS spectral problem and its adjoint spectral problem under an implicit symmetry constraint, we obtain a finite dimensional system from the Lax pair of th... 详细信息

关键词： an implicit symmetry constraint binary nonlinearization AKNS system completely integrable Hamiltonian system

Controlled Secure Quantum Dialogue Using a Pure Entangled GHZ States

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Communications in Theoretical Physics 2007年第5X期48卷 841-846页

作者： XIA Yan song Jie NIE jing song he-Shan School of Physics and Optoelectronic Technology Dalian University of Technology Dalian 116024 China

We present a controlled secure quantum dialogue protocol using a non-maximally （pure） entangled Greenberger-Horne-Zeibinger （GHZ） states at first, and then discuss the requirements for a real quantum dialogue. We show that the authorized two users can exchange their secret messages after purifying the non-maximally entangled GHZ states quantum channel unconditionally securely and simultaneously under the control of a third party.

关键词： controlled secure quantum dialogue eavesdropper non-maximally entangled GHZ state

A New Quantum Communication Scheme by Using Bell States

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Communications in Theoretical Physics 2006年第2期45卷 271-274页

作者： CAO Hai-jing CheN jing song he-Shan Department of Physics Dalian University of Technology Dalian 116024 China

A new quantum communication scheme based on entanglement swapping is presented. Simplified calculation symbols are adopted to realize the process. Quantum key distribution and quantum secure direct communication can be simultaneously accomplished in the scheme. Two legitimate communicators can secretly share four certain key bits and four random key bits via three EPR pairs （quantum channels）.

关键词： quantum key distribution quantum secure direct communication Bell-state measurements security

Quantum Key Distribution Using Four-Qubit W State

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Communications in Theoretical Physics 2006年第1X期46卷 65-68页

作者： CAO Hai-jing song he-Shan Department of Physics Dalian University of Technology Dalian 116024 China

A new theoretical quantum key distribution scheme based on entanglement swapping is proposed, where four-qubit symmetric W state functions as quantum channel. It is shown that two legitimate users can secretly share a... 详细信息

关键词： quantum key distribution W state Bell-state measurement security

Exact solutions of a(2+1)-dimensional extended shallow water wave equation

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Chinese Physics B 2019年第10期28卷 237-244页

作者： Feng Yuan jing-song he Yi Cheng School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026China Institute for Advanced Study Shenzhen UniversityShenzhen 518060China

We give the bilinear form and n-soliton solutions of a（2+1）-dimensional [（2+1）-D] extended shallow water wave（eSWW） equation associated with two functions v and r by using Hirota bilinear method. We provide solitons, breathers,and hybrid solutions of them. Four cases of a crucial φ（y）, which is an arbitrary real continuous function appeared in f of bilinear form, are selected by using Jacobi elliptic functions, which yield a periodic solution and three kinds of doubly localized dormion-type solution. The first order Jacobi-type solution travels parallelly along the x axis with the velocity（3k12+ α, 0） on（x, y）-plane. If φ（y） = sn（y, 3/10）, it is a periodic solution. If φ（y） = cn（y, 1）, it is a dormion-type-Ⅰ solutions which has a maximum（3/4）k1p1 and a minimum-（3/4）k1p1. The width of the contour line is ln■. If φ（y） = sn（y, 1）, we get a dormion-type-Ⅱ solution（26） which has only one extreme value-（3/2）k1p1. The width of the contour line is ln■. If φ（y） = sn（y, 1/2）/（1 + y2）, we get a dormion-type-Ⅲ solution（21） which shows very strong doubly localized feature on（x, y） plane. Moreover, several interesting patterns of the mixture of periodic and localized solutions are also given in graphic way.

关键词： (2+1)-dimensional extended shallow water wave equation Hirota bilinear method dormion-type solution

Recursion Relations for the Constrained Multi-component KP Hierarchy

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Acta Mathematica Sinica,English Series 2017年第11期33卷 1578-1586页

作者： Xu GAO Chuan Zhong LI jing song he Department of Mathematics Ningbo UniversityNingbo 315211P.R.China

In this paper, we define a new constrained multi-component KP （cMKP） hierarchy which contains the constrained KP （cKP） hierarchy as a special case. We derive the recursion operator of the constrained multi-component KP hierarchy. As a special example, we also give the recursion operator of the constrained two-component KP hierarchy.

关键词： Recursion relation the KP hierarchy the constrained KP hierarchy the constrained multi-component KP hierarchy the constrained two-component KP hierarchy

Quantum Teleportation Through a Two-Qubit heisenberg XXZ Chain

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Communications in Theoretical Physics 2008年第6期49卷 1435-1438页

作者： GUO Jin-Liang NIE jing song he-Shan School of Physics and Optoelectronic Technology Dalian University of Technology Dalian 116024 China

We consider a two-qubit heisenberg XXZ chain as a resource for quantum teleportation via the standard teleportation protocol To. The effects of anisotropic on teleportation fidelity and entanglement are studied in detail. We find anisotropic not only improves the criticM temperature Tc and criticM magnetic field Bc, beyond which quantum teleportation is inferior to classicM communication protocol, but also enhances the fidelity for fixed magnetic field B and temperature T. For entanglement teleportation, the effects of magnetic field on average fidelity and output entanglement are studied.

关键词： thermal entanglement negativity two-qubit heisenberg XXZ chain

Surfaces and Curves Corresponding to the Solutions Generated from Periodic“Seed”of NLS Equation

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Acta Mathematica Sinica,English Series 2012年第8期28卷 1713-1726页

作者： Ling ZHANG jing song he Yi CheNG Yi Shen LI Department of Mathematics University of Science and Technology of China Department of Mathematics Chuzhou University Department of Mathematics Ningbo University

The solutions q[n] generated from a periodic ＂seed＂ q = cei（as＋bt） of t：he nonlinear SchrS- dinger （NLS） by n-fold Darboux transformation is represented by determinant. Furthermore, the s-periodic solution and t-periodic solution are given explicitly by using q[1]. The curves and surfaces （F1, F2, F3） associated with q[n] are given by means of Sym formula. Meanwhile, we show periodic and asymptotic properties of these curves.

关键词： Darboux transformation nonlinear SchrSdinger equation integrable surface

General Higher-Order Breather and Hybrid Solutions of the Fokas System

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Communications in Theoretical Physics 2019年第5期71卷 496-508页

作者： Ting-Ting Chen Peng-Yan Hu jing-song he Department of Mathematics Ningbo UniversityNingbo315211China College of Mathematics and Statistics Shenzhen UniversityShenzhen518060China

Fokas system is the simplest(2+1)-dimensional extension of the nonlinear Schr?dinger(NLS) equation(Eq.(2), Inverse Problems 10(1994) L19-L22). By appropriately limiting on soliton solutions generated by the Hirota bilinear method, the explicit forms of n-th breathers and semi-rational solutions for the Fokas system are derived. The obtained first-order breather exhibits a range of interesting dynamics. For high-order breather, it has more rich dynamical behaviors. The first-order and the second-order breather solutions are given graphically. Using the long wave limit in soliton solutions, rational solutions are obtained, which are used to analyze the mechanism of the rogue wave and lump respectively. By taking a long waves limit of a part of exponential functions in f and g appeared in the bilinear form of the Fokas system, many interesting hybrid solutions are constructed. The hybrid solutions illustrate various superposed wave structures involving rogue waves, lumps, solitons, and periodic line waves. Their rather complicated dynamics are revealed.

关键词： Fokas system bilinear method breathers hybrid solutions