Nonlinear Shrodinger Equation Research Articles

Nuclear Decay Oscillations and Nonlinear Quantum Dynamics

Several experimental groups reported the evidence of periodic modulations of nuclear decay constants which amplitudes are of the order $${{10}^{{ - 3}}}$$ and periods of one year, 24 h or about one month. We argue that such deviations from radioactive decay law can be described in nonlinear quantum mechanics framework, in which decay process obeys to nonlinear Shrodinger equation with Doebner–Goldin terms. Possible corrections to Hamiltonian of quantum system interaction with gravitation field considered, it’s shown that they correspond to some emergent gravity theories, in particular, bilocal field model. It’s shown that proposed model describes decay parameter variations which agree with experimental results for Po-214 $$\alpha $$ -decay life-time oscillations.

On Optical Solitons of the Fractional (3+1)-Dimensional NLSE With Conformable Derivatives

In this article, fractional (3+1)-dimensional nonlinear Shrodinger equation is analysed with kerr law nonlinearity. The extended direct algebraic method (EDAM) is applied to obtain the optical solitons of this equation with the aid of conformable derivative. Optical solitons are investigated for this equation with the aid of the EDAM after the nonlinear Shrodinger equation transformes an ordinary di¤erential equation by using the wave variables trans- formation.

Direct Laser Written Waveguide in Tellurite Glass for Supercontinuum Generation in 2 μm Spectral Range

A depressed cladding waveguide composed of 36 parallel tracks is inscribed in high purity 70TeO2-22WO3-8Bi2O3 glass by femtosecond laser operating at 1030 nm. The Sellmeier formula for the refractive index of the investigated glass is obtained for the range of 1170–2350 nm. The module of the negative refractive index change in a track is found to increase with increasing wavelength in the range of 640–2000 nm. The waveguide shows single mode behavior in the wavelength range of 1700–2100 nm with mode field diameter (MFD) of 20 μm. The propagation loss is predominantly due to scattering in the waveguide. Spectrum broadening as large as 503 nm was demonstrated in a 14 mm long waveguide pumped by femtosecond pulses at 1950 nm. In the low input pulse energy region, the spectrum broadening is well described by generalized nonlinear Shrodinger equation (GNLSE) taking into account Kerr and the Raman nonlinearities under the assumption of constant MFD along the waveguide. Under higher energy pumping, an extra broadening was observed that is attributed to the focusing effect of Kerr lens in the waveguide mode.

On the propagation of nonlinear SH waves in a two-layered compressible elastic medium

We examine nonlinear shear horizontal (SH) waves in a two-layered medium of uniform thickness. Materials in both layers having different material properties are assumed to be nonlinear elastic, homogeneous, compressible and isotropic. Furthermore, $$c_1<c_2$$ is chosen where $$c_1$$ and $$c_2$$ are the linear shear wave velocities of the top and bottom layers, respectively. The propagation of SH waves in a two-layered medium exists only if either of the inequalities $$c_1<c< c_2$$ and $$c_1<c_2< c$$ is satisfied where c refers to the phase velocity of waves. The dispersion relations of linear SH waves corresponding to these phase inequalities are obtained. Then, the self-modulation of nonlinear SH waves is investigated by using an asymptotic perturbation method for each case. By balancing dispersion and weak nonlinearity, it is shown that the self-modulation of the first-order slowly varying amplitude of nonlinear SH waves is characterized asymptotically by nonlinear Shrodinger (NLS) equation. The form of NLS equations corresponding to each phase inequality is identical except their coefficients. Then, the effects of nonlinearity of the materials in layers on the linear stability of the solution of NLS equation and on the existence of solitary wave solutions are studied by employing several fictive material parameter models.

Numerical Solution of the Cubic Nonlinear Shrodinger's Equation with Repulsive Delta Potential

Numerical Solution of the Cubic Nonlinear Shrodinger's Equation with Repulsive Delta Potential

Coupled Soliton States and Localization of Cnoidal Waves at the Interface of Nonlinear and Linear Media

Contact effects at the interface of linear and nonlinear media are studied. The problem of different stationary states in two-level system with different parameters of the dispersion relation is considered. A model that employs the nonlinear Shrodinger equation is used to show coupled states of solitons, localization of waves on one side of a defect, and transformation of nonlinear wave into linear wave upon transition through interface for the system under study due to variation in energy. Dispersion relations that determine the energies of such states are derived.

Editorial on Dissipative Optical Solitons

The fundamental mechanism that defines the concept of an optical soliton is the exact balance between two opposite mechanisms, one allowing for the spreading, the other for the concentration of a localized distribution of light. Historically, this was found in conservative systems and can be described by the nonlinear Shrodinger equation and other related equations. This situation applies both to the case of temporal solitons where group velocity dispersion and self-phase modulation counteract one another in the longitudinal dimension of light propagation and to the case of spatial solitons where diffraction spreading and Kerr lensing compensate, leading to a stable distribution of light with a constant beam waist. Solitons have been known as an experimental evidence since the early observation by John Scott Russel of a water solitary wave in 1844. The study of temporal optical solitons more than a century later has benefited from the very rapid development during the 70’s of optical fiber performance whose residual Kerr effect could be used to propagate short intense pulses across distances that can reach now thousands of kilometers. From the 1990’s a new branch of soliton studies has developed in dissipative optical systems defined as lossy systems fed with an external input of energy. Therein, it has been progressively shown through the pioneering theoretical work of Lugiato and Lefever [1], Rosanov [2], Mandel [3], and Firth [4] that nonlinear optical cavities or feedback systems can reach various levels of self-organization among which patterned and localized bistable states are expected. These predictions were rapidly confirmed by their observation in various systems including liquid crystal light valves [5], sodium vapors [6], photorefractive materials [7], and most recently semiconductors [8,9]. These localized states, when exhibiting bistability, were called cavity solitons and appeared to display new properties. The term “soliton”, though not strictly matching the requirement of being an exact solution of a conservative non linear propagation equation, conveys however the concept that an equilibrium is reached between counteracting mechanisms, one of them at least being nonlinear. Indeed, in addition to obtaining

THE STABILITY OF MICROSCOPIC PARTICLES DESCRIBED BY THE NONLINEAR SCHRÖDINGER EQUATION

A nonlinear Schrodinger equation is used to replace the linear Schrodinger equation in quantum mechanics and to study further the stability of microscopic particles by using the minimum theorem of energy and variational theorem. The investigation shows that the microscopic particles described by the nonlinear Shrodinger equation are localized and have a wave–corpuscle duality, which are completely different from that depicted by the linear Schrodinger equation in quantum mechanics. The results obtained by the minimum theorem of energy and variational theorem indicate that the solutions of the nonlinear Schrodinger equation or the microscopic particles are stable. Therefore, the microscopic particles have the feature of classical particles in such a case.

Instability of standing waves of the Schrödinger equation with inhomogeneous nonlinearity

This paper is concerned with the inhomogeneous nonlinear Shrodinger equation (INLS-equation)iu_t + Δu + V(Єx)│u│^pu = 0, x Є R^N. In the critical and supercritical cases p ≥ 4/N, with N ≥ 2, it is shown here that standing-wave solutions of (INLS-equation) on H^1(R^N) perturbation are nonlinearly unstable or unstable by blow-up under certain conditions on the potential term V with a small Є > 0.

Approximate Transformation Groups and Renormgroup Symmetries

An approach that makes use of approximate group symmetries forcalculating renormgroup symmetries for boundary-value problems inmathematical physics is discussed. A comparison of exact and approximatesolutions for the nonlinear Shrodinger equation and quasi-Chaplyginequations is presented that demonstrates promising features of thesuggested approach.

Numerical investigation of self-action effects of backward volume magnetostatic waves confined beams in ferromagnetic films

Self-action effects of backward volume magnetostatic waves confined beams in ferromagnetic films were studied numerically in the framework of nonstationary two-dimensional nonlinear Shrodinger equation. It was found, that for equation coefficients and power levels typical for dipole waves the character of numerical solution corresponds to transverse instability of waves in the form of self-focusing and self-canalization effects. Self-focusing and self-canalization effects of wave beams with different aperture function are quality similar for equal levels of average input power. In case of aperture functions with several local extreme, wave beams self-canalization leads to spatial solution collision effects.

Propagation of a soliton-like pulse in a weakly nonlinear medium

Numerical methods are used to study the decay dynamics of a soliton-like signal in a medium with a cubic nonlinearity (using the nonlinear Shrodinger equation). We consider the influence of the initial pulse area, shape, and random modulations in its amplitude and phase on the decay process, as well as the effects of absorption and pumping in the medium.

High-speed DPSK coherent systems in the presence of chromatic dispersion and Kerr effect

The error probability for a single-channel coherent optical differential phase-shift keying (DPSK) transmission system based on repeaterless links in the presence of fiber chromatic dispersion and Kerr effect is evaluated. An accurate model for both the optical signal propagation and the probability distribution of the receiver decision variable is obtained by using a numerical solution of the nonlinear Shrodinger equation and the characteristic function method. The results show that the selection of an optimized IF filter bandwidth is crucial to obtaining the best system performance. When chromatic dispersion dominates, the best performance is achieved in the normal dispersion region whereas when the Kerr effect has the most limiting effect on system performances, the lowest error probability is attained in the anomalous regime. The maximum link length is limited by the presence of Kerr effect, independently of the amount of transmitted optical power, to be shorter than a threshold length if an error probability of 10/sup -9/ is to be achieved.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On nonlinear water waves under a light wind and Landau type equations near the stability threshold

Various mechanisms of nonlinear saturation of water wave growth under the action of a light wind are discussed. The unstable wind may be saturated by nonlinear dissipation due to the energy transfer to the damping harmonics of the wave. Other nonlinear saturation mechanisms: nonlinear frequency shift, self-modulation or self-focusing of a wave packet may be effective in certain wavenumber regions. In case the wind speed is close to the critical one, an equation is derived for the complex wave amplitude. This equation describes all these nonlinear effects in near-critical systems. In the one-dimensional case this is the nonlinear Shrodinger equation with complex coefficients. Its solutions under various conditions are discussed.