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Register a new userDissipative solitons stabilized by a quantum Zeno-like effect
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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.
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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 ($mathcal{PT}$) symmetric Rosen-Morse potential. In this study, stability of solution is examined by numerical analysis to show that solitons are stable for some parameter ranges for both self-focusing and self-defocusing nonlinear modes. Dynamical properties such as evolution and transverse energy flow for both modes are also analyzed. Obtained results are useful for experimental designs and applications in related fields.
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. Recently, Mamyshev oscillators (MOs), which rely upon a pair of narrow filters with offset passing frequencies, have emerged as a promising candidate for high power, ultrabroad bandwidth pulse generation. To date, only stable mode-locking states in MOs have been reported. Here, we present a comprehensive experimental and numerical investigation of pulsating DSs in an ytterbium MO. By reducing the filter separation down to 4 nm, we observe pulsation in a single pulse state as well as a soliton molecule state. In the single pulse state, the output pulse energy can vary as large as 40 times in our MO. Single-shot spectra measured by the dispersive Fourier transform (DFT) method reveal the spectral bandwidth breathing during pulsation and enables the observation of soliton explosion in a pulsation state. In addition, pulsation with a period lasting 9 round trips and even a chaotic pulsation state are also observed. Numerical simulations based on a lumped model qualitatively agree with our observation. Our results enrich DS dynamics in MOs and show the impact of filter separation on the stability of MOs.
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 flat-floor textquotedblleft bubbles, and topological excitations, in the form of dark solitons in 1D and vortices with winding number $m$ in 2D. Unlike bright solitons, delocalized bubbles and dark modes were not previously considered in this setting. The ground and excited states are accurately approximated by the Thomas-Fermi expressions. The 1D and 2D bubbles, as well as vortices with $m=1$, are completely stable, while the dark solitons and vortices with $m=2$ have nontrivial stability boundaries in their existence areas. Unstable dark solitons are expelled to the periphery, while unstable double vortices split in rotating pairs of unitary ones. Displaced stable vortices precess around the central point.
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 framework to evaluate first-order corrections of the full set of the scattering data within the integrable one-dimensional focusing nonlinear Schrodinger (NLSE) equation. The general scattering data portrait reveals nonlinear coherent structures - solitons - playing the key role in the wavefield evolution. Applying the developed theory to a classic box-shaped wavefield we solve the derived equations analytically for a single Fourier mode acting as a perturbation to the initial condition, thus, leading to the sensitivity closed-form expressions for basic soliton characteristics, i.e. the amplitude, velocity, phase and its position. With the appropriate statistical averaging we model the soliton noise-induced effects resulting in compact relations for standard deviations of soliton parameters. Relying on a concept of a virtual soliton eigenvalue we derive the probability of a soliton emergence or the opposite due to noise and illustrate these theoretical predictions with direct numerical simulations of the NLSE evolution. The presented framework can be generalised to other integrable systems and wavefield patterns.
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 this short note is to survey the conceptual influence of the concept of a production-dissipation (input-output) energy balance that they identified. Our recent results on nonlinear periodic waves as dissipative solitons (in a model equation for a ferrofluid interface in a parallel-flow rectangular geometry subject to an inhomogeneous magnetic field) have shown that the classical concept also applies to nonlocalized (specifically, spatially periodic) nonlinear coherent structures. Thus, we revisit the so-called KdV-KSV equation studied by C. I. Christov and M. G. Velarde to demonstrate that it also possesses spatially periodic dissipative soliton solutions. These coherent structures arise when the linearly unstable flat film state evolves to sufficiently large amplitude. The linear instability is then arrested when the nonlinearity saturates, leading to permanent traveling waves. Although the two model equations considered in this short note feature the same prototypical linear long-wave instability mechanism, along with similar linear dispersion, their nonlinearities are fundamentally different. These nonlinear terms set the shape and eventual dynamics of the nonlinear periodic waves. Intriguingly, the nonintegrable equations discussed in this note also exhibit multiperiodic nonlinear wave solutions, akin to the polycnoidal waves discussed by J. P. Boyd in the context of the completely integrable KdV equation.
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