Im. Moroz et Pk. Newton, PHASE-AMPLITUDE DYNAMICS OF THE NONLINEAR SCHRODINGER-EQUATION WITH RAPID FORCING, Journal of mathematical physics, 36(9), 1995, pp. 4923-4939
We consider the initial value problem for the forced one dimensional n
onlinear Schrodinger equation (NLS), where the forcing is assumed to b
e fast compared to the evolution of the unforced equation. This sugges
ts the introduction of two time scales. Solutions to the forced NLS ar
e sought by expressing the dependent variable in modulus-phase form an
d 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. So
lutions to second order in the expansion are computed analytically for
some specific choices of the forcing function. A general conclusion o
f this work is that the effect of the forcing on the phase variable is
quite important in determining the overall structure of the forced so
litary wave. (C) 1995 American Institute of Physics.