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An unstable particle in quantum mechanics can be stabilized by frequent measurements, known as the quantum Zeno effect. A soliton with dissipation behaves like an unstable particle. Similar to the quantum Zeno effect, here we show that the soliton can be stabilized by modulating periodically dispersion, nonlinearity, or the external harmonic potential available in BEC. This can be obtained by analyzing a Painleve integrability condition, which results from the rigorous Painleve analysis of the generalized nonautonomous nonlinear Schrodinger equation. The result has a profound implication to the optical soliton transmission and the matter-wave soliton dynamics.
We investigate the existence and stability of dissipative soliton solution in a system described by complex Ginzburg-Landau (CGL) equation with asymmetric complex potential, which is obtained from original parity reflection - time reversal ($mathcal{
Mode-locked fiber lasers provide a versatile playground to study dissipative soliton (DS) dynamics. The corresponding studies not only give insights into soliton dynamics in dissipative systems, but also contribute to femtosecond fiber laser design.
We consider one- and two-dimensional (1D and 2D) optical or matter-wave media with a maximum of the local self-repulsion strength at the center, and a minimum at periphery. If the central area is broad enough, it supports ground states in the form of
We investigate the fundamental problem of the nonlinear wavefield scattering data corrections in response to a perturbation of initial condition using inverse scattering transform theory. We present a complete theoretical linear perturbation framewor
In 1995, C. I. Christov and M. G. Velarde introduced the concept of a dissipative soliton in a long-wave thin-film equation [Physica D 86, 323--347]. In the 25 years since, the subject has blossomed to include many related phenomena. The focus of thi