Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2409.01135

Suppression of soliton collapses, modulational instability, and rogue-wave excitation in two-L\'evy-index fractional Kerr media

Ming Zhong·Yong Chen·Zhenya Yan·Boris A. Malomed
View original source ↗Read source document ↗Export metadata ↓

Abstract

s in laser systems with two fractional-dispersion/diffraction terms, quantified by their L\'{e}vy indices, $\alpha_{1}\, \alpha_{2}\in (1, 2]$, and self-focusing or defocusing Kerr nonlinearity. Some fundamental solitons are obtained by means of the variational approximation, which are verified by comparison with numerical results. We find that the soliton collapse, exhibited by the one-dimensional cubic fractional nonlinear Schr\"{o}dinger equation with only one L\'{e}vy index $\alpha =1$, can be suppressed in the two-L\'{e}vy-index fractional nonlinear Schr\"{o}dinger system. Stability of the solitons is also explored against collisions with Gaussian pulses and adiabatic variation of the system parameters. Modulation instability of continuous waves is investigated in the two-L\'{e}vy-index system too. In particular, the modulation instability may occur in the case of the defocusing nonlinearity when two diffraction coefficients have opposite signs. Using results for the modulation instability, we produce first- and second-order rogue waves on top of continuous waves, for both signs of the Kerr nonlinearity.

Explore related subjects

nlin.PSmath-phmath.MPphysics.comp-phphysics.opticsquant-ph

Keep this discovery

BibTeXRIS

Ming Zhong, Yong Chen, Zhenya Yan, Boris A. Malomed. 2024-09-02. Suppression of soliton collapses, modulational instability, and rogue-wave excitation in two-L\'evy-index fractional Kerr media. https://arxiv.org/abs/2409.01135

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Self-similar vector solitons for the coupled higher-order nonlinear Schrodinger equations in inhomogeneous optical fibers

We prove the existence of two kinds of self-similar vector solitons in an inhomogeneous optical fiber medium, where light propagation is governed by a pair of coupled higher-order nonlinear Schrodinger equations with varying second- and third-order dispersions, self- and cross-phase modulation non linearities, self-steepening, and linear gain/loss effects. The newly found self-similar waves comprise bright-W-shaped and kink-antikink waveforms with nonvanishing amplitudes. As a practical exam ple, we discuss the propagation dynamics of these soliton structures in a periodically distributed fiber system as well as an exponential dispersion-decreasing fiber. The results demonstrate that the parameter functions of gain/loss and third-order dispersion serve as a key factor in determining the nonlinear dynamics of self-similar vector solitons. In particular, we find that precise control over the shape and dynamic evolution of self-similar pulses can be achieved through a proper choice of the distributed third-order dispersion parameter, while the gain/loss coefficient controls their intensity.

nlin.PS↗
arXiv2026

Fast Synergetic Simulation to Study Slow Evolution of Soliton Patterns in Optical Resonators

Complex patterns in physical and biological systems often emerge through slow collective dynamics governed by a small number of key variables. In nonlinear optical resonators, dissipative Kerr solitons provide an important example, where interactions between well-separated solitons can evolve over timescales far longer than the characteristic loss and gain timescales. Direct numerical simulation of these dynamics is challenging because stiffness forces conventional methods to resolve many rapidly damped degrees-of-freedom with very small time steps. We present a numerical scheme, the synergetic method, that eliminates these rapidly damped degrees-of-freedom and retains the slowly evolving modes, enabling time steps many orders of magnitude larger than those used in conventional approaches. Applied to soliton molecules in driven Kerr cavities, the method achieves speedups of $10^3$ to $10^5$ while capturing dynamics on laboratory timescales. We use it to model the full interaction dynamics of a three-soliton molecule and the evolution of an eight-soliton molecule. The approach provides an efficient framework for studying slow pattern formation in nonlinear systems with widely separated timescales.

nlin.PS↗
arXiv2026

Breathers in solitonic room-temperature superlattice-induced superfluorescence in quasi-2D perovskites

Recently, a soliton mechanism for room-temperature superfluorescence in thin perovskite films has been proposed, with a fundamental soliton predicted to remain stable under LO phonon--exciton interactions. At the same time, superlattice architectures offer a route to enhancing superfluorescence in perovskites. Motivated by recent observations of room-temperature superfluorescence in periodic superlattices of quasi-2D metal-halide perovskites, we extend the 2D nonlocal nonlinear Schr\"odinger equation describing Wannier exciton--LO phonon interactions to superlattice structures, obtaining a 3D nonlocal nonlinear Schr\"odinger equation. We show that interlayer tunnelling gives rise to breather dynamics corresponding to a stable fundamental soliton in mixed coordinate--momentum space, with the coordinate parallel to the layers and the momentum perpendicular to them. The breather dynamics originate from miniband formation, which induces a momentum-dependent phase modulation of the soliton. In the absence of interlayer tunnelling, the breather dynamics disappear and the soliton becomes stationary. These results establish a direct connection between interlayer tunnelling, miniband formation and soliton dynamics, suggesting that breather behavior can provide a signature of interlayer tunnelling in quasi-2D perovskite superlattices.

nlin.PS↗