TY - JOUR
T1 - On analytic families of invariant tori for PDEs
JF - AstÃ©risque. Issue 297, 2004, Pages 35-65
Y1 - 2004
A1 - Boris Dubrovin
AB - We propose to apply a version of the classical Stokes\\r\\nexpansion method to the perturbative construction of invariant tori for\\r\\nPDEs corresponding to solutions quasiperiodic in space and time variables.\\r\\nWe argue that, for integrable PDEs all but finite number of the\\r\\nsmall divisors arising in the perturbative analysis cancel. As an illustrative\\r\\nexample we establish such cancellations for the case of KP equation.\\r\\nIt is proved that, under mild assumptions about decay of the magnitude\\r\\nof the Fourier modes all analytic families of finite-dimensional invariant\\r\\ntori for KP are given by the Krichever construction in terms of thetafunctions\\r\\nof Riemann surfaces. We also present an explicit construction\\r\\nof infinite dimensional real theta-functions and corresponding quasiperiodic\\r\\nsolutions to KP as sums of infinite number of interacting plane\\r\\nwaves.
PB - SISSA
UR - http://hdl.handle.net/1963/6474
U1 - 6420
U2 - Mathematics
U4 - 1
U5 - MAT/07 FISICA MATEMATICA
ER -