Existence and perturbation of embedded solitones governed by a extension of the NLS equation

Abstract

We determine the conditions for the existence of "embedded solitons" (ES), and conventional bright and dark pulses, in an extension of the cubic nonlinear Schrodinger (NLS) equation with higher-order dispersive and nonlinear terms. The stability of these SE is studied numerically, and it is found that these solitons are semi-stable. The damped oscillatory behavior of the perturbed SE is then analyzed by variational method, and it is shown that this damping is a consequence of the emission of radiation. Finally, it is shown that the uniqueness of these SE is due to a delicate balance between nonlinearity and dispersion.