Ba. Malomed et al., RESONANT SHAPE OSCILLATIONS AND DECAY OF A SOLITON IN A PERIODICALLY INHOMOGENEOUS NONLINEAR-OPTICAL FIBER, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 48(2), 1993, pp. 1418-1425
The propagation of a soliton in a nonlinear optical fiber with a perio
dically modulated but sign-preserving dispersion coefficient is analyz
ed by means of the variational approximation. The dynamics are reduced
to a second-order evolution equation for the width of the soliton tha
t oscillates in an effective potential well in the presence of a perio
dic forcing induced by the imhomogeneity. This equation of motion is c
onsidered analytically and numerically. Resonances between the oscilla
tions in the potential well and the external forcing are analyzed in d
etail. It is demonstrated that regular forced oscillations take place
only at very small values of the amplitude of the inhomogeneity; the o
scillations become chaotic as the inhomogeneity becomes stronger and,
when the dimensionless amplitude attains a threshold value which is ty
pically less than 1/4 the soliton is completely destroyed by the perio
dic inhomogeneity.