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 maps.To characterise the chaotic behaviour of this system,the spectra of the Lyapunov exponent and Lyapunov dimension of the attractor are also employed.
Starting from a weak Lax pair,the general Lie point symmetry group of the Konopelchenko-Dubrovsky equation is obtained by using the general direct method.And the corresponding Lie algebra structure is proved to be a Kac-Moody-Virasoro type.Furthermore,a new multi-soliton solution for the Konopelchenko-Dubrovsky equation is also given from this symmetry group and a known solution.
