With the help of a Lie algebra, an isospectral Lax pair is introduced for which a new Liouville integrable hierarchy of evolution equations is generated. Its Hamiltonian structure is also worked out by use of the quad...With the help of a Lie algebra, an isospectral Lax pair is introduced for which a new Liouville integrable hierarchy of evolution equations is generated. Its Hamiltonian structure is also worked out by use of the quadratic-form identity.展开更多
Spiral waves, whose rotation center can be regarded as a point defect, widely exist in various two-dimensional excitable systems. In this paper, by making use of Duan＇s topological current theory, we obtain the charg...Spiral waves, whose rotation center can be regarded as a point defect, widely exist in various two-dimensional excitable systems. In this paper, by making use of Duan＇s topological current theory, we obtain the charge density of spiral waves and the topological inner structure of its topological charge. The evolution of spiral wave is also studied from the topological properties of a two-dimensional vector field. The spiral waves are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the two-dimensional vector field. Some applications of our theory are also discussed.展开更多
A new type of homoclinic arid heteroclinic solutions, i.e. homoclinic and heteroclinic breather solutions, for Zakharov system are obtained using extended homoclinic test and two-soliton methods, respectively. Moreove...A new type of homoclinic arid heteroclinic solutions, i.e. homoclinic and heteroclinic breather solutions, for Zakharov system are obtained using extended homoclinic test and two-soliton methods, respectively. Moreover, the homoclinic and heteroclinic structure with local oscillation and mechanicaL feature different from homoclinic and heterocliunic solutions are investigated. Result shows complexity of dynamics for complex nonlineaR evolution system. Moreover, the similarities and differences between homoclinic （heteroclinic） breather and homoclinic （heteroclinic） tube are exhibited. These results show that the diversity of the structures of homoclinic and heteroclinic solutions.展开更多
文摘With the help of a Lie algebra, an isospectral Lax pair is introduced for which a new Liouville integrable hierarchy of evolution equations is generated. Its Hamiltonian structure is also worked out by use of the quadratic-form identity.
基金supported by National Natural Science Foundation of China and the Cuiying Programme of Lanzhou University
文摘Spiral waves, whose rotation center can be regarded as a point defect, widely exist in various two-dimensional excitable systems. In this paper, by making use of Duan＇s topological current theory, we obtain the charge density of spiral waves and the topological inner structure of its topological charge. The evolution of spiral wave is also studied from the topological properties of a two-dimensional vector field. The spiral waves are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the two-dimensional vector field. Some applications of our theory are also discussed.
基金Supported by the Natural Science Foundation of China under Grant No.11061028
文摘A new type of homoclinic arid heteroclinic solutions, i.e. homoclinic and heteroclinic breather solutions, for Zakharov system are obtained using extended homoclinic test and two-soliton methods, respectively. Moreover, the homoclinic and heteroclinic structure with local oscillation and mechanicaL feature different from homoclinic and heterocliunic solutions are investigated. Result shows complexity of dynamics for complex nonlineaR evolution system. Moreover, the similarities and differences between homoclinic （heteroclinic） breather and homoclinic （heteroclinic） tube are exhibited. These results show that the diversity of the structures of homoclinic and heteroclinic solutions.
