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On Integrable Properties for Two Variable-Coefficient Evolution Equations

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Communications in Theoretical Physics 2013年第6期59卷 671-678页

作者： ZHANG Yu-Feng HAN Zhong honwah tam College of Sciences China University of Mining and Technology Xuzhou 221116 China Department of Computer Science Hong Kong Baptist University Hong Kong China

With the help of the extended binary Bell polynomials, the new bilinear representations, Backlund trans- formations, Lax pair and infinite conservation laws for two types of variable-coefficient nonlinear integrable equations are obtained, respectively, which are more straightforward than previous corresponding results obtained. Finally, we obtain new multi-soliton wave solutions of a reduced soliton equations with variable coefficients.

关键词： Bell polynomials Backlund transformation conservation laws

Lie Algebras Associated with Group U（n）

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Communications in Theoretical Physics 2007年第2X期48卷 215-226页

作者： ZHANG Yu-Feng DONG Huang-He honwah tam Mathematical School Liaoning Normal University Dalian 116029 China School of Information and Science Engineering Shandong University of Science and Technology Qingdao 266510 China Department of Computer Science Hong Kong Baptist University Hong Kong China

Starting from the subgroups of the group U（n）, the corresponding Lie algebras of the Lie algebra Al are presented, from which two well-known simple equivalent matrix Lie algebras are given. It follows that a few expanding Lie algebras are obtained by enlarging matrices. Some of them can be devoted to producing double integrable couplings of the soliton hierarchies of nonlinear evolution equations. Others can be used to generate integrable couplings involving more potential functions. The above Lie algebras are classified into two types. Only one type can generate the integrable couplings, whose Hamiltonian structure could be obtained by use of the quadratic-form identity. In addition, one condition on searching for integrable couplings is improved such that more useful Lie algebras are enlightened to engender. Then two explicit examples are shown to illustrate the applications of the Lie algebras. Finally, with the help of closed cycling operation relations, another way of producing higher-dimensional Lie algebras is given.

关键词： Lie algebra group integrable couplings

Higher-Dimensional KdV Equations and Their Soliton Solutions

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Communications in Theoretical Physics 2006年第3期45卷 411-413页

作者： ZHANG Yu-Feng tam honwah ZHAO Jing School of Mathematics Liaoning Normal University Dalian 116029 China Department of Computer Sciences Hong Kong Baptist University Hong Kong China Information School Dalian University Dalian 116622 China

A （2＋1）-dimensional KdV equation is obtained by use of Hirota method, which possesses N-soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and the Riccati equation, a type of hell-shape soliton solutions are produced via regarding the variable in the Riccati equation as the independent variable. Finally, we extend the above （2＋1）-dimensional KdV equation into （3＋1）-dimensional equation, the two-soliton solutions are given.

关键词： bilinear operator KdV equation soliton equation