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Chinese Physics B 2008年第2期17卷 403-410页

作者：张亮张立凤李崇银 Institute of Meteorology PLA University of Science and TechnologyLaboratory of Applied Geophysics State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric PhysicsChinese Academy of Sciences

By using the modified mapping method, we find some new exact solutions of the generalized Boussinesq equation and the Boussinesq-Burgers equation. The solutions obtained in this paper include jacobian elliptic functio... 详细信息

关键词： generalized Boussinesq equation Boussinesq-Burgers equation jacobian elliptic function modified mapping method

Exact jacobian elliptic function Solutions to sinh-Gordon Equation

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Communications in Theoretical Physics 2006年第1期45卷 55-60页

作者： FU Zun-Tao LIU Shi-Kuo LIU Shi-Da School of Physics Peking University Beijing 100871 China State Key Laboratory for Turbulence and Complex Systems Peking University Beijing 100871 China

In this paper, two transformations are introduced to solve sinh-Gordon equation by using the knowledge of elliptic equation and jacobian elliptic functions. It is shown that different transformations are required in o... 详细信息

关键词： jacobian elliptic function transformation sinh-Gordon equation

Some New Exact Solutions of jacobian elliptic function of Petviashvili Equation

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Communications in Theoretical Physics 2008年第6期49卷 1557-1560页

作者： ZHANG Ling ZHANG Li-Feng LI Chong-Yin WANG Tie TAN Yan-Ke Institute of Meteorology PLA University of Science and Technology Laboratory of Applied Geophysics Nanjing 211101 China State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics the Chinese Academy of Sciences Beijing 100029 China

By using the modified mapping method, we find new exact solutions of the Petviashvili equation. The solutions obtained in this paper include jacobian elliptic function solutions, combined jacobian elliptic function so... 详细信息

关键词： Petviashvili equation jacobian elliptic function modified mapping method

General jacobian elliptic function expansion method and its applications

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Chinese Physics B 2004年第6期13卷 798-804页

作者：朱加民马正义方建平郑春龙张解放 DepartmentofPhysics ZhejiangLishuiNormalCollegeLishui323000China ShanghaiInstituteofAppliedMathematicsandMechanics Shanghai200072China InstituteofNonlinearPhysics ZhejiangNormalUniversityJinhua321004China

An extended jacobian elliptic function expansion method is presented and successfully applied to the nonlinear Schr(o)dinger (NLS) equation and Zakharov equation. We obtain some new solutions besides Fu et al's results. The results show that our method is more powerful to construct jacobian elliptic function and can be applied to othernonlinear physics systems.

关键词： nonlinear Schr(o)dinger equation Zakharov equation jacobian elliptic function solitary wave solution

Rogue waves for the(2+1)-dimensional Myrzakulov–Lakshmanan-Ⅳ equation on a periodic background

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Communications in Theoretical Physics 2024年第4期76卷 32-42页

作者： Xiao-Hui Wang Zhaqilao College of Mathematics Science Inner Mongolia Normal UniversityHohhot 010022China Laboratory of Infinite-dimensional Hamiltonian System and Its algorithm Application Hohhot 010022China Center for Applied Mathematical Science Inner MongoliaHohhot 010022China

In this paper, the rogue wave solutions of the(2+1)-dimensional Myrzakulov–Lakshmanan(ML)-Ⅳ equation, which is described by five component nonlinear evolution equations, are studied on a periodic background. By using the jacobian elliptic function expansion method, the Darboux transformation(DT) method and the nonlinearization of the Lax pair, two kinds of rogue wave solutions which are expressed by jacobian elliptic functions dn and cn, are *** relationship between these five kinds of potential is summarized systematically. Firstly, the periodic rogue wave solution of one potential is obtained, and then the periodic rogue wave solutions of the other four potentials are obtained directly. The solutions we find present the dynamic phenomena of higher-order nonlinear wave equations.

关键词： rogue waves on a periodic background (2+1)-dimensional Myrzakulov-Lakshmanan-IV equation Darboux transformation jacobian elliptic function

Fractal　localized　structures　related　to　jacobian　elliptic　functions　in　the　higher-order　Broer-Kaup　system

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Chinese Physics B 2004年第9期13卷 1382-1385页

作者：马正义朱加民郑春龙 DepartmentofPhysicsandMathematics LishuiUniversityLishui323000China InstituteofAppliedMathematicsandMechanics ShanghaiUniversityShanghai200072China

This work reveals a novel phenomenon-that the localized coherent structures of a (2+1)-dimensional physical model possesses fractal behaviours. To clarify the interesting phenomenon, we take the (2+1)-dimensional higher-order Broer-Kaup system as a concrete example. Starting from a Backlund transformation, we obtain a linear equation, and then a general solution of the system is derived. From this some special localized excitations with fractal behaviours are obtained by introducing some types of lower-dimensional fractal patterns that related to jacobian elliptic functions.

关键词： higher-order Broer-Kaup system Backlund transformation variable separation approach jacobian elliptic function fractal

非线性振动、非线性波与Jacobi椭圆函数(续)

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大学物理 2004年第1期23卷 3-7,24页

作者：佘守宪北京交通大学物理系北京100044

Succinct and efficient method to obtain analytic solutions of nonlinear vibrations and nonlinear waves by jacobian elliptic functions are introduced. Important typical examples are given and explained, including simple pendulum, Duffing oscillator, cnoidal wave and solitary wave solutions of KdV equation, sine-Gordon equation, nonlinear Schrdinger equation, sech^2 profile solitons, kink and anti-kink solitons, breather, interaction of a kink and an anti-kink, and envelop solitons.

关键词： nonlinear vibration simple pendulum Duffing oscillator solitary waves jacobian elliptic function

Breather Lattice Solutions to Negative mKdV Equation

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Communications in Theoretical Physics 2009年第7期52卷 23-29页

作者： ZHAO Xia FU Zun-Tao MAO Jiang-Yu LIU Shi-Kuo College of Atmospheric Science Lanzhou University Lanzhou 730000 China School of Physics ＆ State Key Laboratory for Turbulence and Complex Systems Peking University Beijing 100871 China LASG Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 China School of Physics Peking University Beijing 100871 China

In this paper,dependent and independent variable transformations are introduced to solve the negativemKdV equation systematically by using the knowledge of elliptic equation and jacobian elliptic *** is shownthat different kinds of solutions can be obtained to the negative mKdV equation,including breather lattice solution andperiodic wave solution.

关键词： jacobian elliptic function the negative mKdV equation periodic wave solution breather lattice solution

Separation Transformation and New Exact Solutions of the (N+1)-dimensional Dispersive Double sine-Gordon Equation

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Communications in Theoretical Physics 2012年第9期58卷 398-404页

作者：田野陈静张志飞 Department of Physics College of ScienceHebei North University School of Applied Mathematics Central University of Finance and Economics Department of Mathematics and Statistics Huazhong University of Science and Technology

In this paper, the separation transformation approach is extended to the （N ＋ 1）-dimensional dispersive double sine-Gordon equation arising in many physical systems such as the spin dynamics in the B phase of SHe superfluid. This equation is first reduced to a set of partial differential equations and a nonlinear ordinary differential equation. Then the general solutions of the set of partial differential equations are obta/ned and the nonlinear ordinary differential equation is solved by F-expansion method. Finally, many new exact solutions of the （N ＋ 1）-dimensional dispersive double sine-Gordon equation are constructed explicitly via the separation transformation. For the case of N 〉 2, there is an arbitrary function in the exact solutions, which may reveal more novel nonlinear structures in the high-dimensional dispersive double sine-Gordon equation.

关键词： dispersive double sine-Gordon equation separation transformation jacobian elliptic function F-expansion method

Exact Solutions to Degasperis-Procesi Equation

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Communications in Theoretical Physics 2008年第7期50卷 48-50页

作者： ZHANG Lin-Na FU Zun-Tao LIU Shi-Kuo School of Physics ＆ Laboratory for Severe Storm and Flood Disaster Peking University Beijing 100871 China State Key Laboratory for Turbulence and Complex Systems Peking University Beijing 100871 China

In this paper,dependent and independent variable transformations are introduced to solve the Degasperis-Procesi *** is shown that different kinds of solutions can be obtained to the Degasperis-Procesi equation.

关键词： jacobian elliptic function Degasperis Procesi equation transformation