Bound states of envelope solitons

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Abstract
It has been demonstrated recently that weakly overlapping solitons in the dissipatively perturbed nonlinear Schrödinger (NS) equation may form a set of bound states (BS’s). In this work, it is demonstrated that additional ‘‘skew’’ dissipative terms, which occur in various applications, e.g., a term describing the stimulated Raman scattering in a nonlinear optical fiber, destroy all the BS’s provided the corresponding coefficient exceeds a certain critical value. Next, taking as an example the dissipationless NS equation with the higher linear dispersion, it is demonstrated that two solitons or a whole array of them may form BS’s, interacting with each other via emitted radiation. Then, it is shown that the sine-Gordon (SG) breathers, governed by the standard damped ac-driven equation, may form BS’s quite similarly to the NS solitons. At last, interactions of damped NS or SG solitons supported by a parametric ac drive are analyzed, and it is inferred that they, unlike the directly supported solitons, cannot form BS’s.