Vey theorem in infinite dimensions and its application to KdV
Vey theorem in infinite dimensions and its application to KdV
We consider an integrable infinite-dimensionalHamiltonian system in a Hilbert space$H=\{u=(u_1^+,u_1^-; u_2^+,u_2^-;....)\}$with integrals $I_1, I_2,....$ which can be writtenas $I_j=\frac{1}{2}|F_j|^2$, where $F_j:H\rightarrow \R^2$,$F_j(0)=0$ for $j=1,2,....$We assume that the maps $F_j$ define a germ of an analytic diffeomorphism$F=(F_1,F_2,...):H\rightarrow H$,such that $dF(0)=id$, $(F-id)$ is a $\kappa$-smoothing map ($\kappa\geq 0$)and some other mild restrictions …