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A method of expansion of solutions of singularly perturbed nonlinear systems in power series of small parameters is applied to the popular Lorenz model in synergetics.Simple asymptotic expressions for the solution to the model in…
Traveling modulating pulse solutions consist of a small amplitude pulse-like envelope moving with a constant speed and modulating a harmonic carrier wave. Such solutions can be approximated by solitons of an effective nonlinear Schrodinger…
We report on the observation of modulation instability induced by cross-phase modulation in a dual-wavelength operation dispersion-managed soliton fiber ring laser with net negative cavity dispersion. The passively mode-locked operation is…
We are concerned with the study of the system of coupled equations of motion for a system of two-level atoms interacting with a single-mode field in the laser cavity on resonance. The passage from the equation of motion to the Lorenz…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
We propose a time-dependent partial differential equation model to investigate the dynamical behavior of the parity-time (PT) symmetric laser during the nonlinear stage of its operation. This model incorporates physical effects such as the…
A general coupled-wave model is presented for square-lattice photonic crystal (PC) lasers with transverse-electric polarization. This model incorporates the high-order coupling effects that are important for two-dimensional PC laser…
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…
We present a novel laser mode-locking scheme and discuss its unusual properties and feasibility using a theoretical model. A large set of single-frequency continuous-wave lasers oscillate by amplification in spatially separated gain media.…
The mixed nonlinear Schr\"odinger (MNLS) equation is a model for the propagation of the Alfv\'en wave in plasmas and the ultrashort light pulse in optical fibers with two nonlinear effects of self-steepening and self phase-modulation(SPM),…
The nonlinear Schr\"{o}dinger (NLS) equation can be derived as a formal approximation equation describing the envelopes of slowly modulated spatially and temporarily oscillating wave packet-like solutions to the ion Euler-Poisson equation.…
In this article, we construct novel explicit solutions for nonlinear Schr\"odinger systems with spatially inhomogeneous nonlinearity by means of the Lie symmetry method. We focus the attention to solutions with non-trivial phase, which have…
The paper presents soliton-breather models of particles tunneling on the example of Klein-Gordon and Schrodinger equation nonlinear breathers. It is shown that in this case the non-linearity registration should lead to spatial restrictions…
We make an adaptation of laser modelling equations to describe the behavior of a phonon laser (saser). Our saser consists of an AlGaAs/GaAs double barrier heterostructure designed to generate an intense beam of transversal acoustic (TA)…
In this paper we study the smoothness properties of solutions to a one-dimensional coupled nonlinear Schr\"{o}dinger system equations that describes some physical phenomena such as propagation of polarized laser beams in birefringent Kerr…
We further develop the method of dressing the boundary for the focusing nonlinear Schr\"odinger equation (NLS) on the half-line to include the new boundary condition presented by Zambon. Additionally, the foundation to compare the solutions…
Nonlinear Schr\"odinger equation, complemented by a confining potential, possesses a discrete set of stationary solutions. These are called coherent modes, since the nonlinear Schr\"odinger equation describes coherent states. Such modes are…
Holographically-designed aperiodic lattices have proven to be an exciting engineering technique for achieving electrically switchable single- or multi-frequency emissions in terahertz (THz) semiconductor lasers. Here, we employ the…
In this paper we show a systematical method to obtain exact solutions of the nonautonomous nonlinear Schr\"odinger (NLS) equation. An integrable condition is first obtained by the Painlev\`e analysis, which is shown to be consistent with…
Laser-generated plasma gratings are dynamic optical elements for the manipulation of coherent light at high intensities, beyond the damage threshold of solid-stated based materials. Their formation, evolution and final collapse require a…