摘要：Hamiltonian symmetry group (R＞0)N generated through a family of conserved integrals is proposed. Themethod of invariants is used to reduce the binary nonlinearized Toda spectral problem on R4N into a 3 × 3 nonlinearized spectral problem with a Lie-Poisson structure on R4N/(R＞0)N. Furthermore, it is shown that the 3 × 3 one restricted on the common level set of cones is a usual 2 × 2 mono-nonlinearized spectral problem.%利用Hamilton對稱群的作用不變量,將R4N上具有標準辛結構的雙非線性化Toda特征值問題約化為R4N/(R＞0)N上Lie-Poisson結構下的3×3非線性化特征值問題;并進一步討論了該3×3非線性化特征值問題與R2N上標準辛結構下的2×2非線性化特征值問題之間的關系.
摘要：A new symmetric form of the equations of MHD transverse flow(MHDTF) is presented. On the basis,the local existence of smooth solution in the case where the initial density tends to vacuum state is obtained by using of treatment technique for hyperbolic equations. Furthermore,the global smooth solutions for a kind of initial data are obtained.%利用分析技巧得到磁流體力學方程組新的對稱形式.在此基礎上,在初始密度趨于真空狀態假設下,利用處理雙曲方程組的方法證明了經典解的局部存在性,進而得到了經典解的整體存在性.
