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Communications in Theoretical Physics 2008年第2期49卷 275-280页

作者： JIA Man Department of Physics Shanghai Jiao Tong University Shanghai 200240 China Department of Physics North China Coal Medical College Tangshan 063000 China

Using Ablowitz-Ramani Segur algorithm, the coupled KdV systems are reclassified under the Painlevé integrable sense while the similarity reductions of the model are obtained by using the Clarkson and Kruskal＇s direct method. Some new types of Painlevé integrable models including a model with different dispersion relations for two layer fluids are found.

关键词： coupled KdV equation Painlevé classification similarity reductions

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Communications in Theoretical Physics 2009年第6期51卷 1083-1090页

作者： WANG Jia LI Biao Nonlinear Science Center and Department of Mathematics Ningbo University Ningbo 315211 China MM Key Lab Chinese Academy of Sciences Beijing 100080 China

Basing on the direct method developed by Clarkson and Kruskal, the nearly concentric Korteweg-de Vries （ncKdV） equation can be reduced to three types of （1＋1）-dimensional variable coefficients partial differential equations （PDEs） and three types of variable coefficients ordinary differential equation. Furthermore, three types of （1＋1）-dimensional variable coefficients PDEs are all reduced to constant coefficients PDEs by some transformations.

关键词： nearly concentric KdV equation CK direct method similarity reductions

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Communications in Theoretical Physics 2008年第1期49卷 229-230页

作者： TANG Xiao-Yan Padma Kant Shukla Department of Physics Shanghai Jiao Tong University Shanghai 200240 China Institut fur Theoretische Physik IV Fakultat fur Physik und Astronomie Ruhr-Universitat Bochum D-44870 Bochum Germany School of Physics University of KwaZulu-Natal 4000 Durban South Africa

Applying the classical Lie symmetry approach to the barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a β-plane channel, we find a new symmetry, which is not presented in a previous work [F. Huang, Commun. Theor. Phys. （Beijing, China） 42 （2004） 903]. A general finite transformation group is obtained based on the full Lie point symmetry, Furthermore, two new types of similarity reduction solutions are obtained.

关键词： Lie symmetry similarity reductions potential vorticity equation

Symmetries and similarity reductions of a New (2+1)-Dimensional Shallow Water Wave System

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Communications in Theoretical Physics 2008年第3期49卷 555-558页

作者： LIU Ping Department of Physics Shanghai Jiao Tong University Shanghai 200240 China

The symmetries of a （2＋1）-dimensional shallow water wave system, which is newly constructed through applying variation principle of analytic mechanics, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. The （1＋1） dimensional displacement shallow water wave equation can be derived from the reductions when special symmetry parameters are chosen.

关键词： (2+1)-dimensional shallow water wave system classical Lie group approach symmetries similarity reductions

Time-fractional Davey–Stewartson equation:Lie point symmetries,similarity reductions,conservation laws and traveling wave solutions

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Communications in Theoretical Physics 2023年第10期75卷 10-25页

作者： Baoyong Guo Yong Fang Huanhe Dong College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao266590China

As a celebrated nonlinear water wave equation,the Davey–Stewartson equation is widely studied by researchers,especially in the field of mathematical *** the basis of the Riemann–Liouville fractional derivative,the time-fractional Davey–Stewartson equation is investigated in this *** application of the Lie symmetry analysis approach,the Lie point symmetries and symmetry groups are *** the same time,the similarity reductions are ***,the equation is converted to a system of fractional partial differential equations and a system of fractional ordinary differential equations in the sense of Riemann–Liouville fractional *** virtue of the symmetry corresponding to the scalar transformation,the equation is converted to a system of fractional ordinary differential equations in the sense of Erdélyi–Kober fractional integro-differential *** using Noether’s theorem and Ibragimov’s new conservation theorem,the conserved vectors and the conservation laws are ***,the traveling wave solutions are achieved and plotted.

关键词： time-fractional Davey–Stewartson equation Lie symmetry analysis approach Lie point symmetries similarity reductions conservation laws

Symmetry Analysis of Nonlinear Incompressible Non-Hydrostatic Boussinesq Equations

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Communications in Theoretical Physics 2010年第4期53卷 609-614页

作者：刘萍高晓楠 Department of Electronic Engineering University of Electronic Science and Technology of China Zhongshan Institute Department of Physics Shanghai Jiao Tong University

The symmetries of the （2＋1）-dimensional nonlinear incompressible non-hydrostatic Boussinesq （INHB） equations, which describe the atmospheric gravity waves （GWs）, are researched in this paper. The Lie symmetries and the corresponding reductions are obtained by means of classical Lie group approach. Calculation shows the INHB equations are invariant under some Galilean transformations, scaling transformations, and space-time translations. The symmetry reduction equations and similar solutions of the INHB equations are proposed.

关键词： incompressible non-hydrostatic Boussinesq equations classical Lie group approach symmetries similarity reductions atmospheric gravity waves

General Solution and Fractal Localized Structures for the （2＋1）—Dimensional Generalized Ablowitz—Kaup—Newell—Segur System

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Chinese Physics Letters 2002年第10期19卷 1399-1402页

作者： ZHENGChun-Long ZHANGJie-Fang 等 DepartmentofPhysics ZhejiangLishuiNormalCollegeLishui323000 DepartmentofPhysics ZhejiangUniversityHangzhou310028

Using the standard truncated Painlevé expansions, we derive a quite general solution of the (2+1)-dimensional generalized Ablowitz-Kaup-Newell-Segur system. Except for the usual localized solutions, such as dromions, lumps, ring soliton solutions, etc, some special localized excitations with fractal behaviour, *** fractal dromion and fractal lump excitations, are obtained by some types of lower-dimensional fractal patterns.

关键词： NONLINEAR SCHRODINGER-EQUATION COHERENT STRUCTURES similarity reductions BOUSSINESQ EQUATION EVOLUTION-EQUATIONS DROMION SOLITONS INTEGRABILITY SCATTERING PLASMA

Peakon and Foldon Excitations in a （2＋1）—Dimensional Breaking Soliton System

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Chinese Physics Letters 2003年第6期20卷 783-786页

作者： ZHENGChun-Long ZHANGJie-Fang HUANGWen-Hua CHENLi-Qun ShanghaiInstituteofMathematicsandMechanics ShanghaiUniversityShanghai200072 InstituteofNonlinearPhysics ZhejiangNormalUniversityJinhua321004

Starting from the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the breaking soliton system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, and previously revealed chaotic and fractal localized solutions, some new types of excitations, peakons and foldons, are obtained by introducing appropriate lower-dimensional piecewise smooth functions and multiple valued functions.

关键词： LOOP SOLITON PAINLEVE INTEGRABILITY similarity reductions GENERAL-SOLUTION FIELDS

Symmetries and Exact Solutions of the Breaking Soliton Equation

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Communications in Theoretical Physics 2011年第11期56卷 851-855页

作者：陈美刘希强 School of Mathematical Sciences Liaocheng University

With the aid of the classical Lie group method and nonclassical Lie group method,we derive the classicalLie point symmetry and the nonclassical Lie point symmetry of (2+1)-dimensional breaking soliton (BS)*** symmetries,we find six classical similarity reductions and two nonclassical similarity reductions of the BS *** of exact solutions of the BS equation are obtained by solving the reduced equations.

关键词： breaking soliton equation symmetry similarity reductions exact solutions