Author： Korotyaev Evgeny L.
Publisher： Oxford University Press
ISSN： 1073-7928
Source： International Mathematics Research Notices, Vol.2013, Iss.10, 2013-04, pp. : 2203-2239
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Abstract
We consider the defocussing nonlinear Schrdinger equation (NLS) equation with small periodic initial condition. A new approach to study the Hamiltonian as a function of action variables is demonstrated. The problems for the NLS equation are reformulated as the problems of conformal mapping theory corresponding to the quasimomentum of the ZakharovShabat operator. The main tool is the Lwner-type equation for the quasimomentum. In particular, we determine the asymptotics of the Hamiltonian for small action variables. Moreover, we determine the gradient of Hamiltonian with respect to action variables. This gives so-called frequencies and determines how the angles variables depend on the time.
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