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We revisit the averaged equation, derived in Phys. Rev. Lett. 91, 240201 (2003)] from the nonlinear Schrödinger (NLS) equation with the nonlinearity management. We show that this averaged equation is valid only at the initial time interval, while a new Hamiltonian averaged NLS equation can be used at longer time intervals. Using the new averaged equation,… (More)
Near linear evolution in Korteweg de Vries (KdV) equation with periodic boundary conditions is established under the assumption of high frequency initial data. This result is obtained by the method of normal form reduction.
A system of two coupled pendula is an example of a Hamiltonian system with two degrees of freedom. Rott considered such a system in the presence of 1:2 resonance and observed a phase-locking phenomenon. In this paper this phenomenon is explained by means of Duistermaat's method of bringing a Hamiltonian system with two degrees of freedom into standard form.… (More)