The Painlevé Analysis And Integrability For Finite And Infinite Dimensional Systems

Painlevé analysis is a useful method for studying nonlinear differential equation.A four dimensional Lorenz system with Hamiltonian function H considered in the paper. The system is studied by means ofPainlevé analysis. The expanded singular manifold for the system is truncated bymeans of resonances. Therefore it is proved that the system is a Painlevé integrablesystem. The B cklund transformation is found and some exact solutions of the systemare obtained by solving Schwarz equation.A22spectral problem is considered. A hierarchy of soliton equation isreduced. It is proved that the soliton equation is Painlevé integrable. The B cklundtransformation of the equation is obtained. We also study the modifiedJaulent-Miodek equation and STO system by means of Painlevé analysis.