Abstract
In this paper, we study the efficient solution of the nonlinear Schrödinger equation with wave operator, subject to periodic boundary conditions. In such a case, it is known that its solution conserves a related functional. By using a Fourier expansion in space, the problem is at first casted into Hamiltonian form, with the same Hamiltonian functional. A Fourier–Galerkin space semi-discretization then provides a large-size Hamiltonian ODE problem, whose solution in time is carried out by means of energy-conserving methods in the HBVM class (Hamiltonian boundary value methods). The efficient implementation of the methods for the resulting problem is also considered and some numerical examples are reported.
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