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- W2962936855 abstract "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 $F_j:Hrightarrow R^2$,$F_j(0)=0$ for $j=1,2,....$We assume that the maps $F_j$ define a germ of an analytic diffeomorphism$F=(F_1,F_2,...):Hrightarrow H$,such that $dF(0)=id$, $(F-id)$ is a $kappa$-smoothing map ($kappageq 0$)and some other mild restrictions on $F$ hold.Under these assumptions we show that the maps $F_j$may be modified to maps F ’j such that$F_j-$F ’j$=O(|u|^2)$ and each 1/2|F ’j|$^2$ still is an integral of motion.Moreover, these maps jointlydefine a germ of an analyticsymplectomorphism F’$: Hrightarrow H$, the germ (F’-id) is $kappa$-smoothing, and each $I_j$ isan analytic function of the vector (1/2|F’j|$^2,jge1)$. Next we show that the theorem with $kappa=1$applies to the KdV equation.It implies that in the vicinity of the origin in a functional spaceKdV admits the Birkhoff normal form and the integratingtransformation has the form'identity plus a 1-smoothing analytic map'." @default.
- W2962936855 created "2019-07-30" @default.
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- W2962936855 date "2010-01-01" @default.
- W2962936855 modified "2023-10-15" @default.
- W2962936855 title "Vey theorem in infinite dimensions and its application to KdV" @default.
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