By using a six-dimensional matrix Lie algebra [Y.F.Zhang and Y.Wang,Phys.Lett.A 360 (2006) 92], three induced Lie algebras are constructed.One of them is obtained by extending Lie bracket,the others are higher- dimens...By using a six-dimensional matrix Lie algebra [Y.F.Zhang and Y.Wang,Phys.Lett.A 360 (2006) 92], three induced Lie algebras are constructed.One of them is obtained by extending Lie bracket,the others are higher- dimensional complex Lie algebras constructed by using linear transformations.The equivalent Lie algebras of the later two with multi-component forms are obtained as well.As their applications,we derive an integrable coupling and quasi-Hamiltonian structure of the modified TC hierarchy of soliton equations.展开更多
Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution...Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution for （2＋1）-dimensional ANNV equation. The behaviors of interactions are discussed in detail both analytically and graphically. It is shown that there are two kinds of singular interactions between line soliton and algebraic soliton： 1） the resonant interaction where the algebraic soliton propagates together with the line soliton and persists infinitely; 2） the extremely repulsive interaction where the algebraic soliton affects the motion of the line soliton infinitely apart.展开更多
文摘By using a six-dimensional matrix Lie algebra [Y.F.Zhang and Y.Wang,Phys.Lett.A 360 (2006) 92], three induced Lie algebras are constructed.One of them is obtained by extending Lie bracket,the others are higher- dimensional complex Lie algebras constructed by using linear transformations.The equivalent Lie algebras of the later two with multi-component forms are obtained as well.As their applications,we derive an integrable coupling and quasi-Hamiltonian structure of the modified TC hierarchy of soliton equations.
基金National Natural Science Foundation of China under Grant No.10675065the Science Research Foundation of the Education Department of Zhejiang Province under Grant No.20070979+1 种基金the Natural Science Foundation of Zhejiang Province under Grant No.Y604036the State Key Laboratory of Oil/Gas Reservoir Geology and Exploitation\PLN0402
文摘Starting from the variable separation approach, the algebraic soliton solution and the solution describing the interaction between line soliton and algebraic soliton are obtained by selecting appropriate seed solution for （2＋1）-dimensional ANNV equation. The behaviors of interactions are discussed in detail both analytically and graphically. It is shown that there are two kinds of singular interactions between line soliton and algebraic soliton： 1） the resonant interaction where the algebraic soliton propagates together with the line soliton and persists infinitely; 2） the extremely repulsive interaction where the algebraic soliton affects the motion of the line soliton infinitely apart.
