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Explicit Breather-Type and Pure N-Soliton Solution of DNLS^+ Equation with Nonvanishing Boundary Condition

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Wuhan University Journal of Natural Sciences 2013年第2期18卷 147-155页

作者： zhou guoquan School of Physics and Technology Wuhan University

Based on a newly revised inverse scattering transform for the derivative nonlinear SchrSdinger （DNLS＋） equation with nonvanishing boundary condition （NVBC）, the explicit breather- type and pure N-soliton solution has been derived by some algebra techniques. The two-breather solution and the pure double-soliton solution have been given as two typical examples in illustration of the general formula of the multi-soliton solution. The asymptotic behaviors of the N-soliton solution are discussed in detail.

关键词： soliton breather nonlinear equation derivativenonlinear Schr6dinger equation inverse scattering transform Zakharov-Shabat equation

Fractional Fourier transform of Lorentz-Gauss vortex beams

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Science China(Physics,Mechanics & Astronomy) 2013年第8期56卷 1487-1494页

作者： zhou guoquan WANG XiaoGang CHU XiuXiang School of Sciences Zhejiang A & F University Lin'an 311300 China

An analytical expression for a Lorentz-Gauss vortex beam passing through a fractional Fourier transform (FRFT) system is derived. The influences of the order of the FRFT and the topological charge on the normalized intensity distribution, the phase distribution, and the orbital angular momentum density of a Lorentz-Gauss vortex beam in the FRFT plane are examined. The order of the FRFT controls the beam spot size, the orientation of the beam spot, the spiral direction of the phase distribution, the spatial orientation of the two peaks in the orbital angular momentum density distribution, and the magnitude of the orbital angular momentum density. The increase of the topological charge not only results in the dark-hollow region becoming large, but also brings about detail changes in the beam profile. The spatial orientation of the two peaks in the orbital angular momentum density distribution and the phase distribution also depend on the topological charge.

关键词： Lorentz-Gauss vortex beam fractional Fourier transform orbital angular momentum density

Hollow vortex Gaussian beams

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Science China(Physics,Mechanics & Astronomy) 2013年第5期56卷 896-903页

作者： zhou guoquan CAI YangJian DAI ChaoQing School of Sciences Zhejiang A & F University School of Physical Science and Technology Soochow University

A kind of hollow vortex Gaussian beam is introduced. Based on the Collins integral, an analytical propagation formula of a hollow vortex Gaussian beam through a paraxial ABCD optical system is derived. Due to the special distribution of the optical field, which is caused by the initial vortex phase, the dark region of a hollow vortex Gaussian beam will not disappear upon propagation. The analytical expressions for the beam propagation factor, the kurtosis parameter, and the orbital angular mo- mentum density of a hollow vortex Gaussian beam passing through a paraxial ABCD optical system are also derived, respec- tively. The beam propagation factor is determined by the beam order and the topological charge. The kurtosis parameter and the orbital angular momentum density depend on beam order n, topological charge m, parameter y, and transfer matrix ele- ments A and D. As a numerical example, the propagation properties of a hollow vortex Gaussian beam in free space are demonstrated. The hollow vortex Gaussian beam has eminent propagation stability and has crucial application prospects in op- tical micromanipulation.

关键词： hollow vortex Gaussian beam beam propagation factor kurtosis parameter orbital angular momentum density

A Newly Revised Inverse Scattering Transform for DNLS^(+) Equation under Nonvanishing Boundary Condition

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Wuhan University Journal of Natural Sciences 2012年第2期17卷 144-150页

作者： zhou guoquan School of Physics and Technology Wuhan UniversityWuhan 430072HubeiChina

A newly revised inverse scattering transform（IST） for the derivative nonlinear Schrdinger（DNLS＋） equation with non-vanishing boundary condition（NVBC） and normal group velocity dispersion is proposed by introducing a suitable affine parameter in Zakharov-Shabat integral *** explicit breather-type one-soliton solution,which can reproduce one pure soliton at the de-generate case and one bright soliton solution at the limit of van-ishing boundary,has been derived to verify the validity of the revised IST.

关键词： soliton nonlinear equation derivative nonlinear Schrodinger equation inverse scattering transform Zakharov-Shabat equation

Space Periodic Solutions and Rogue Wave Solution of the Derivative Nonlinear Schrodinger Equation

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Wuhan University Journal of Natural Sciences 2017年第5期22卷 373-379页

作者： zhou guoquan LI Xujun School of Physics and Technology Wuhan UniversityWuhan430072HubeiChina

The derivative nonlinear Schrodinger equation, which is extensively applied in plasma physics and nonlinear optics, is analytically studied by Hirota method. Space periodic solutions are determined by means of Hirota＇s bilinear formalism, and the rogue wave solution is derived as a long-wave limit of the space periodic solution.

关键词： bilinear method the derivative nonlinear Schr?d-inger(DNLS) equation space periodic solution rogue wave

Mixed Breather-Type and Pure Soliton Solution of DNLS Equation

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Wuhan University Journal of Natural Sciences 2017年第3期22卷 223-232页

作者： LI Xujun zhou guoquan School of Physics and Technology Wuhan University

A newly revised inverse scattering transform（IST） is used to solve the derivative nonlinear Schr？dinger（DNLS-＋） equation with non-vanishing boundary condition（NVBC） and normal group-velocity dispersion, and a mixed type of soliton solution is found, which is composed of both pure and breather-type solitons. The mixed-soliton solution can degenerate into breathers and pure solitons when taking the limit of some special parameters, proving the validity of the mixed-type solution.

关键词： soliton breather nonlinear Schr?dinger equation inverse scattering transform Zakharov-Shabat equation

Angular momentum density of a Gaussian vortex beam

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Science China(Physics,Mechanics & Astronomy) 2014年第4期57卷 619-627页

作者： zhou guoquan WANG XiaoGang DAI ChaoQing CHU XiuXiang School of Sciences Zhejiang A & F University

The Gaussian vortex beam is assumed to be linearly *** analytical expression of the electric field of a linearly polarized Gaussian vortex beam propagating in free space is derived by using the vectorial Rayleigh-Sommerfeld integral *** propagating magnetic field of the linearly polarized Gaussian vortex beam is presented by taking the curl of the electric *** employing the electromagnetic field of the linearly polarized Gaussian vortex beam beyond the paraxial approximation,the analytical expression of the angular momentum density of the linearly polarized Gaussian vortex beam is *** three components of the angular momentum density of a linearly polarized Gaussian vortex beam are demonstrated in the reference *** effects of the linearly polarized angle and the topological charge on the three components of the angular momentum density are *** acquire the more longitudinal angular momentum density requires such an optimal choice that the linearly polarized angle is set to be zero and the topological charge *** research is useful to the optical trapping,the optical guiding,and the optical manipulation.

关键词： Gaussian vortex beam angular momentum density linearly polarized angle topological charge

Soliton Solution of the DNLS Equation Based on Hirota's Bilinear Derivative Transform

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Wuhan University Journal of Natural Sciences 2009年第6期14卷 505-510页

作者： zhou guoquan BI Xintao School of Physics and Technology Wuhan UniversityWuhan 430072 Hubei China School of Physics China University of Science andTechnology Hefei 230026 Anhui China

Based on the method of Hirota＇s bilinear derivative transform, the derivative nonlinear Schrodinger equation with vanishing boundary condition has been directly solved. The oneand two-soliton solutions are given as two typical examples in the illustration of the general procedures and the concrete cut-off technique of the series-form solution, and the n-soliton solution is also attained by induction method. Our study shows their equivalence to the existing soliton solutions by a simple parameter transformation. The methodological importance of bilinear derivative transform in dealing with an integrable nonlinear equation has also been emphasized. The evolution of one and two-soliton solution with respect to time and space has been discussed in detail. The collision among the solitons has been manifested through an example of two-soliton case, revealing the elastic essence of the collision and the invariance of the soliton form and characteristics.

关键词： soliton nonlinear equation derivative nonlinear Schrodinger equation Hirota's method bilinear derivative transform

Power and Damping Torque of Electric-Quadrupole Radiation for Rotational Charged Rigid Bodies

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Wuhan University Journal of Natural Sciences 2021年第4期26卷 331-338页

作者： zhou guoquan ZENG Weihao LIU Runsheng School of Physics and Technology Wuhan UniversityWuhan 430072HubeiChina School of Physics Peking UniversityBeijing 100871China

Based on the basic theory of electrodynamics about electromagnetic radiation,the general formulae of radiation power and damping torque of electric-quadrupole moment for a steadily and uniformly charged rigid body with any periodic rotation are *** concise form of the formulae in some special symmetric cases are deduced and discussed,and the results of several common symmetric charged bodies are listed.

关键词： electromagnetic radiation electric-quadrupole moment damping torque damping rotation rigid body