Related papers: Predicting instabilities of a tuneable ring laser …
A new nonlinear model is proposed for tuneable lasers. Using the generalized nonlinear Schr\"odinger equation as a starting point, expressions for the transformations undergone by the pulse are derived for each of the five components (gain,…
The linear instability of thin, vertically-isothermal Keplerian discs, under the influence of axial magnetic field is investigated. Solutions of the stability problem are found explicitly by asymptotic expansions in the small aspect ratio…
The propagation of stable coherent entities of an electromagnetic field in nonlinear media with parameters varying in space can be described in the framework of iterations of nonlinear integral transformations. It is shown that for a set of…
In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and…
We analyze the modulational instability of nonlinear Bloch waves in topological photonic lattices. In the initial phase of the instability development captured by the linear stability analysis, long wavelength instabilities and bifurcations…
Propagation of ultrashort pulses at least a few tens of optical cycles in duration through a negative index material is investigated theoretically based on the generalized nonlinear Schr\"{o}dinger equation with pseudo-quintic nonlinearity…
We investigate analytically, numerically, and experimentally the modulational instability in a layered, cubically-nonlinear (Kerr) optical medium that consists of alternating layers of glass and air. We model this setting using a nonlinear…
The magnetorotational instability (MRI) is a fundamental process of accretion disk physics, but its saturation mechanism remains poorly understood despite considerable theoretical and computational effort. We present a multiple scales…
We introduce a complete analytical and numerical study of the modulational instability process in a system governed by a canonical nonlinear Schr\"odinger equation involving local, arbitrary nonlinear responses to the applied field. In…
Effects of nonlinearity in Thomson scattering of a high intensity laser pulse from electrons are analyzed. Analytic expressions for laser pulse shaping in amplitude and frequency are obtained which control spectrum broadening for…
Inspired by the classical Poincar\'e criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the variational properties of periodic…
Pulse train instabilities have often given rise to confusion in misinterpretation in ultrafast pulse characterization measurements. Most prominently known as the coherent artifact, a partially mode-locked laser with non-periodic waveform…
Modulation instability in a nonlinear optical waveguide array with alternating positive and negative refractive indices is investigated analytically. Particular solutions of a system of coupled nonlinear equations are found. These solutions…
We prove stability estimates for the recovery of the nonlinearity from the scattering or modified scattering map for one-dimensional nonlinear Schr\"odinger equations. We consider nonlinearities of the form $a(x) |u|^p u$ for $p\in [2,4]$…
Mapper is an unsupervised machine learning algorithm generalising the notion of clustering to obtain a geometric description of a dataset. The procedure splits the data into possibly overlapping bins which are then clustered. The output of…
Invariant manifolds of unstable periodic orbits organize the dynamics of chaotic orbits in phase space. They provide insight into the mechanisms of transport and chaotic advection and have important applications in physical situations…
The dynamics and stability of continuous-wave and multi-pulse structures are studied theoretically, for a generalized model of passively mode-locked fiber laser with an arbitrary nonlinearity. The model is characterized by a complex…
The modulational instability of broadband optical pulses in a four-state atomic system is investigated. In particular, starting from a recently derived generalized nonlinear Schr\"odinger equation, a wave-kinetic equation is derived. A…
We present a new, more nuanced understanding of non-linear effects in inverse Compton sources. Contrary to what has been heretofore understood, deleterious non-linear effects can arise even at low laser intensities, a regime previously…
We subject the stationary solutions of inviscid and axially symmetric rotational accretion to a time-dependent radial perturbation, which includes nonlinearity to any arbitrary order. Regardless of the order of nonlinearity, the equation of…