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Solitary Wave Solutions for the Coupled Ito System and a Generalized Hirota-Satsuma Coupled KdV System

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Communications in Theoretical Physics 2001年第12期36卷 657-660页

作者： zhang yu-feng Department of Applied Mathematics Dalian University of Technology Dalian 116024 China

We make use of an extended tanh-function method and symbolic computation to construct four kinds of travelling solitary wave solutions for the coupled Ito system and a generalized Hirota-Satsuma coupled KdV *** number... 详细信息

关键词： coupled Ito system generalized Hirota-Satsuma coupled KdV system travelling solitary wave solution symbolic computation waves Solitary waves

Induced Lie Algebras of a Six-Dimensional Matrix Lie Algebra

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Communications in Theoretical Physics 2008年第8期50卷 289-294页

作者： zhang yu-feng LIU Jing Mathematical School Liaoning Normal University Dalian 116029 China

By using a six-dimensional matrix Lie algebra [*** and ***,***.A 360 (2006) 92], three induced Lie algebras are *** of them is obtained by extending Lie bracket,the others are higher- dimensional complex Lie algebras constructed by using linear *** equivalent Lie algebras of the later two with multi-component forms are obtained as *** their applications,we derive an integrable coupling and quasi-Hamiltonian structure of the modified TC hierarchy of soliton equations.

关键词： Lie algebra soliton equation Hamiltonian structure

EFFECT OF INSTABILITIES OF FLOW ON MESOSCALE PREDICTABILITY OF WEATHER SYSTEMS

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Journal of Hydrodynamics 2011年第2期23卷 193-203页

作者： LUO yu zhang Li-feng Institute of Meteorology PLA University of Science and Technology Nanjing 211101

The numerical solution of Boussinesq equations is worked out as an initial-value problem to study the effect of the instabilities of flow on the initial error growth and mesoscale predictability. The development of weather systems depends on different dynamic instability mechanisms according to the spatial scales of the system and the development of mesoscale systems is determined by symmetric instability. Since symmetric instability dominates among the three types of dynamic instability, it makes the prediction of the associated mesoscale systems more sensitive to initial uncertainties. This indicates that the stronger instability leads to faster initial error growth and thus limits the mesoscale predictability. Besides dynamic instability, the impact of thermodynamic instability is also explored. The evolvement of convective instability manifests as dramatic variation in small spatial scale and short temporal scale, and furthermore, it exhibits the upscale growth. Since these features determine the initial error growth, the mesoscale systems arising from convective instability are less predictable and the upscale error growth limits the predictability of larger scales. The latent heating is responsible for changing the stability of flow and subsequently influencing the error growth and the predictability.

关键词： instabilities of flow mesoscale system predictability initial errors

A Type of New Loop Algebra and a Generalized Tu Formula

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Communications in Theoretical Physics 2009年第1期51卷 39-46页

作者： GUO Fu-Kui zhang yu-feng Information School Shandong University of Science and Technology Qingdao 266510 China

A new Lie algebra, which is far different form the known An-1, is established, for which the corresponding loop algebra is given. From this, two isospectral problems are revealed, whose compatibility condition reads a kind of zero curvature equation, which permits Lax integrable hierarchies of soliton equations. To aim at generating Hamiltonian structures of such soliton-equation hierarchies, a beautiful Killing-Cartan form, a generalized trace functional of matrices, is given, for which a generalized Tu formula （GTF） is obtained, while the trace identity proposed by Tu Guizhang [J. Math. Phys. 30 （1989） 330] is a special case of the GTF. The computing formula on the constant γ to be determined appearing in the GTF is worked out, which ensures the exact and simple computation on it. Finally, we take two examples to reveal the applications of the theory presented in the article. In details, the first example reveals a new Liouville-integrable hierarchy of soliton equations along with two potential functions and Hamiltonian structure. To obtain the second integrable hierarchy of soliton equations, a higher-dimensional loop algebra is first constructed. Thus, the second example shows another new Liouville integrable hierarchy with 5-potential component functions and bi- Hamiltonian structure. The approach presented in the paper may be extensively used to generate other new integrable soliton-equation hierarchies with multi-Hamiltonian structures.

关键词： Lie algebra loop algebra Tu formula Hamiltonian structure

Characteristic Numbers of Matrix Lie Algebras

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Communications in Theoretical Physics 2008年第4期49卷 845-850页

作者： zhang yu-feng FAN En-Gui Mathematical School Liaoning Normal University Dalian 116029 China Institute of Mathematics Fudan University Shanghai 200433 China

A notion of characteristic number of matrix Lie algebras is defined, which is devoted to distinguishing various Lie algebras that are used to generate integrable couplings of soliton equations. That is, the exact classification of the matrix Lie algebras by using computational formulas is given. Here the characteristic numbers also describe the relations between soliton solutions of the stationary zero curvature equations expressed by various Lie algebras.

关键词： characteristic number Lie algebra integrable couplings

Matrix Lie Algebras and Integrable Couplings

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Communications in Theoretical Physics 2006年第5X期46卷 812-818页

作者： zhang yu-feng GUO Fu-Kui Mathematical School Liaoning Normal University Dalian 116029 China Information School Shandong University of Science and Technology Qingdao 266510 China

Three kinds of higher-dimensional Lie algebras are given which can be used to directly construct integrable couplings of the soliton integrable systems. The relations between the Lie algebras are discussed. Finally, the integrable couplings and the Hamiltonian structure of Giachetti-Johnson hierarchy and a new integrable system are obtained, respectively.

关键词： Lie algebra integrable couplings GJ hierarchy

An Improved Time Domain Approach for Analysis of Floating Bridges Based on Dynamic Finite Element Method and State-Space Model

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China Ocean Engineering 2022年第5期36卷 682-696页

作者： XIANG Sheng CHENG Bin zhang feng-yu TANG Miao State Key Laboratory of Ocean Engineering Shanghai Jiao Tong UniversityShanghai 200240China Shanghai Key Laboratory for Digital Maintenance of Buildings and Infrastructure Shanghai Jiao Tong UniversityShanghai 200240China Department of Civil Engineering Shanghai Jiao Tong UniversityShanghai 200240China College of Civil Engineering Fuzhou UniversityFuzhou 350108China

The floating bridge bears the dead weight and live load with buoyancy,and has wide application prospect in deep-water transportation *** structural analysis of floating bridge is challenging due to the complicated fluid-solid coupling effects of wind and *** this research,a novel time domain approach combining dynamic finite element method and state-space model(SSM)is established for the refined analysis of floating *** dynamic coupled effects induced by wave excitation load,radiation load and buffeting load are carefully ***-precision fitted SSMs for pontoons are established to enhance the calculation efficiency of hydrodynamic radiation forces in time *** dispersion relation is also introduced in the analysis model to appropriately consider the phase differences of wave loads on *** proposed approach is then employed to simulate the dynamic responses of a scaled floating bridge model which has been tested under real wind and wave loads in *** numerical results are found to agree well with the test data regarding the structural responses of floating bridge under the considered environmental *** proposed time domain approach is considered to be accurate and effective in simulating the structural behaviors of floating bridge under typical environmental conditions.

关键词： floating bridge time domain analysis dynamic analysis state-space model environmental load

Two Types of New Solutions to KdV Equation

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Communications in Theoretical Physics 2006年第4X期46卷 577-579页

作者： GUO Fu-Kui zhang yu-feng Information School Shandong University of Science and Technology Qingdao 266510 China Mathematical School Liaoning Normal University Dalian 116029 China

It is common knowledge that the soliton solutions u（x, t） defined by the bell-shape form is required to satisfy the following condition lira u（x, t） = u（±∞, t） = 0. However, we think that the above condition can be modified as lim u（x, t） = u（±∞, t）^x→ = c, where c is a constant, which is called as a stationary height of u（x, t） in the present paper.^x→∞ If u（x, t） is a bell-shape solitary solution, then the stationary height of each solitary wave is just c. Under the constraint c = 0, all the solitary waves coming from the N-bell-shape-sollton solutions of the KdV equation are the same-oriented travelling. A new type of N-soliton solution with the bell shape is obtained in the paper, whose stationary height is an arbitrary constant c. Taking c ≥ 0, the resulting solitary wave is bound to be the same-oriented travelling. Otherwise, the resulting solitary wave may travel at the same orientation, and also at the opposite orientation. In addition, another type of singular rational travelling solution to the KdV equation is worked out.

关键词： soliton solution Hirota method bilinear differential equation

A Higher-Dimensional Hirota Condition and Its Judging Method

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Communications in Theoretical Physics 2008年第1期49卷 27-30页

作者： GUO Fu-Kui zhang yu-feng Information School Shandong University of Science and Technology Qingdao 266510 China

When a one-dimensional nonlinear evolution equation could be transformed into a bilinear differential form as F（Dt, Dx）f . f = O, Hirota proposed a condition for the above evolution equation to have arbitrary N-soliton solutions, we call it the 1-dimensional Hirota condition. As far as higher-dimensional nonlinear evolution equations go, a similar condition is established in this paper, also we call it a higher-dimensional Hirota condition, a corresponding judging theory is given. As its applications, a few two-dimensional KdV-type equations possessing arbitrary N-soliton solutions are obtained.

关键词： Hirota condition KdV equation soliton solution