In this paper, lower bounds of the topological entropy for nonautonomous dynamical systems are given via the growths of topological complexity in fundamental group and in degree.
In this paper, by using symbolic and algebra computation, Chen and Wang＇s multiple R/ccati equations rational expansion method was further extended. Many double soliton-like and other novel combined forms of exact so...In this paper, by using symbolic and algebra computation, Chen and Wang＇s multiple R/ccati equations rational expansion method was further extended. Many double soliton-like and other novel combined forms of exact solutions of the （2＋1）-dimensional Breaking soliton equation are derived by using the extended multiple Riccatl equations expansion method.展开更多
A 3 × 3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra A^-2. Furthermore, high-order binary symmetry constraints of the corresponding hi...A 3 × 3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra A^-2. Furthermore, high-order binary symmetry constraints of the corresponding hierarchy are obtained by using the binary nonlinearization method. Finally, according to another new subalgebra of loop algebra A^-2, its integrable couplings are established.展开更多
In this paper, a new completely integrable system related to the complex spectral problem -φ xx＋（i/4）wpx＋（i/4）（wp）x＋（1/4）vφ=iλφxand the constrained flows of the Boussinesq equations axe generated. Accor...In this paper, a new completely integrable system related to the complex spectral problem -φ xx＋（i/4）wpx＋（i/4）（wp）x＋（1/4）vφ=iλφxand the constrained flows of the Boussinesq equations axe generated. According to the viewpoint of Hamiltonian mechanics, the Euler-Lagrange equations and the Legendre transformations, a reasonable Jacobi-Ostrogradsky coordinate system is obtained. Moreover, by means of the constrained conditions between the potentiaJ u, v and the eigenfunction φ, the involutive representations of the solutions for the Boussinesq equation hieraxchy axe given.展开更多
基金Supported by the National Natural Science Foundation of China (10701032)Natural Science Foundation of Hebei Province (A2008000132)the Doctoral Foundation of Hebei Normal University (L2005B02)
文摘In this paper, lower bounds of the topological entropy for nonautonomous dynamical systems are given via the growths of topological complexity in fundamental group and in degree.
基金The project partially supported by National Natural Science Foundation of China under Grant No. 10471143 and the State 973 Project under Grant No. 2004CB318001 The authors are very grateful to Prof. Hong-Bo Li, Yong Chen, Zhen-Ya Yan, and Zhuo-Sheng Lii for their kind help and valuable suggestions. They also thank Prof. En-Gui Fan and Prof. Chun-Ping Liu for their constructive suggestions about the solutions of Riccati equation.
文摘In this paper, by using symbolic and algebra computation, Chen and Wang＇s multiple R/ccati equations rational expansion method was further extended. Many double soliton-like and other novel combined forms of exact solutions of the （2＋1）-dimensional Breaking soliton equation are derived by using the extended multiple Riccatl equations expansion method.
基金supported by China Postdoctoral Science Foundation and National Natural Science Foundation of China under Grant No.10471139
文摘A 3 × 3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra A^-2. Furthermore, high-order binary symmetry constraints of the corresponding hierarchy are obtained by using the binary nonlinearization method. Finally, according to another new subalgebra of loop algebra A^-2, its integrable couplings are established.
文摘In this paper, a new completely integrable system related to the complex spectral problem -φ xx＋（i/4）wpx＋（i/4）（wp）x＋（1/4）vφ=iλφxand the constrained flows of the Boussinesq equations axe generated. According to the viewpoint of Hamiltonian mechanics, the Euler-Lagrange equations and the Legendre transformations, a reasonable Jacobi-Ostrogradsky coordinate system is obtained. Moreover, by means of the constrained conditions between the potentiaJ u, v and the eigenfunction φ, the involutive representations of the solutions for the Boussinesq equation hieraxchy axe given.
