Abstract
We consider the initial value problem for the forced one dimensional nonlinear Schrödinger equation (NLS), where the forcing is assumed to be fast compared to the evolution of the unforced equation. This suggests the introduction of two time scales. Solutions to the forced NLS are sought by expressing the dependent variable in modulus-phase form and expanding in powers of a small parameter, which is inversely related to the forcing time scale. This system is similar to a forced eikonal-transport system arising in nonlinear geometrical optics. We focus on the effect that the forcing has on the NLS standing solitary wave. Solutions to second order in the expansion are computed analytically for some specific choices of the forcing function. A general conclusion of this work is that the effect of the forcing on the phase variable is quite important in determining the overall structure of the forced solitary wave.
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