This paper considers the generalized KdV equation with or without natural boundary conditions and provides a parameter region for solitons and solitary waves, and also modifies a result of Zabuskys. The solitary bifur...This paper considers the generalized KdV equation with or without natural boundary conditions and provides a parameter region for solitons and solitary waves, and also modifies a result of Zabuskys. The solitary bifurcation has been discussed.展开更多
The dynamical behaviour of the generalized Korteweg-de Vries （KdV） equation under a periodic perturbation is investigated numerically. The bifurcation and chaos in the system are observed by applying bifurcation dia...The dynamical behaviour of the generalized Korteweg-de Vries （KdV） equation under a periodic perturbation is investigated numerically. The bifurcation and chaos in the system are observed by applying bifurcation diagrams, phase portraits and Poincar＇e maps. To characterise the chaotic behaviour of this system, the spectra of the Lyapunov exponent and Lyapunov dimension of the attractor are also employed.展开更多
基金Research partially supported by Shanghai Development Grant of Education Committee(# 2 0 0 0 A1 0 )
文摘This paper considers the generalized KdV equation with or without natural boundary conditions and provides a parameter region for solitons and solitary waves, and also modifies a result of Zabuskys. The solitary bifurcation has been discussed.
基金Project supported by the National Natural Science Foundation of China (Grant No. 10875078)the Natural Science Foundation of Zhejiang Province,China (Grant No. Y7080455)
文摘The dynamical behaviour of the generalized Korteweg-de Vries （KdV） equation under a periodic perturbation is investigated numerically. The bifurcation and chaos in the system are observed by applying bifurcation diagrams, phase portraits and Poincar＇e maps. To characterise the chaotic behaviour of this system, the spectra of the Lyapunov exponent and Lyapunov dimension of the attractor are also employed.
