Dispersive optical solitons by the semi-inverse variational principle

In this paper an analytical expression for an optical soliton is obtained with the aid of He's semi-inverse variational principle in the presence of third- and fourth-order dispersion as well as inter-modal dispersion. Three laws of nonlinear media are considered in this paper: the Kerr law, the power law and the log law.     

Routes to various breather solitons in whispering-gallery-mode resonators through the variational method

In this paper, the dynamics of the optical field in the whispering-gallery-mode resonator described by the Lugiato–Lefever equation is studied by means of the variational method. For some special cases, exact explicit family of analytical breather-type solitons, such as time-periodic breather and space-time periodic breather are obtained. It is found that the pumping parameter, the detuning parameter and the dispersion coefficient, influences the nature of the optical field in the whispering-gallery-mode resonators.     

Optical solitons to the nonlinear Shrödinger’s equation with spatio-temporal dispersion using complex amplitude ansatz

In this work, we investigate the optical solitons to the non-linear Shrödinger’s equation with spatio-temporal dispersion. There are two types of non-linear media studied in this paper. They are Kerr law and parabolic law. By adopting a complex amplitude ansatz method composed of the addition of bright and dark optical solitons, we present the exact dark, bright and dark-bright or combined optical solitons to the model. Numerical results and discussions are also presented.     

光纤中光孤子传输演化及相互作用研究

基于非线性薛定谔方程,采用分步傅立叶方法模拟了基阶、二阶和三阶皮秒光孤子以及光孤子对在光纤中的传输演化.结果表明,在长距离传输过程中基阶孤子的幅度和脉宽基本不变,是进行光孤子通信的理想载体.高阶孤子的幅度和脉宽变化较大,并呈现一种周期性的变化;孤子对的传输与两个脉冲的初始相位和输入强度相关.考虑三阶色散的飞秒量级孤子在光纤中的传输将不再出现对称性和周期性,脉冲的中心位置将发生偏移,同时脉冲的波形也会发生扭曲.     

Theoretical study of dark solitons in media with competing nonlocal nonlinearities and local quintic nonlinearity

Dark solitons, in a medium with competing nonlocal nonlinearities and local quintic nonlinearity, have been studied analytically in this paper. The phenomenological rectangular profile model for nonlocal response function is considered. The exact conditions for the existence of analytical dark soliton solutions are presented using variational principle. The influence of strengths and degrees of competing nonlocality as well as the strength of quintic locality, on the properties of dark solitons, are discussed.     

Determination of magnetic moment vectors distributions in FeCo/Mn superlattices

We present in details a method for determining non-collinear orders in metallic superlattices and the interlayer magnetic couplings between ferromagnetic layers separated by antiferromagnetic spacers. A semiempirical tight binding framework and the real space recursion technique is used to obtain the electronic structure of non-symmetric systems. We focus on the angular self-consistency and we discuss the angular stability of the solutions obtained by fixing the magnetic moment direction of some atoms. We give a few examples of calculations for bulk Mn and FeCo/Mn superlattices and discuss the validity of the results.     

Semi-analytical method for designing finite sets of discriminated solitons and soliton molecules in fibres

An infinite number of solitons, as well as soliton molecules belonging different families, are allowed to propagate stably along a given dispersion-managed optical fibre. In this paper, we propose a semi-analytical method to systematically find a finite number of solitons and two-soliton molecules. Determined solitons and soliton molecules present a greatest power gap between them, to make them sufficiently distinct symbols for encoding several bits of information per symbol in a multilevel modulation format in fibre-optic transmission systems. Furthermore, for illustrative purposes, we discuss the possibility of encoding three bits per symbol.     

Tailored dispersion profile in controlling optical solitons in a tapered parabolic index fiber

We investigate the soliton dynamics in tapered parabolic index fibers via symbolic computation for a variety of dispersion profiles to inspect how a specific dispersion profile controls the optical soliton. By means of AKNS procedure, Lax pair is constructed for nonlinear Schrödinger equation with variable coefficients. Using obtained Lax pair, multi-soliton solutions are generated via Darboux transformation technique. Using multi-soliton solutions, soliton dynamics in tapered parabolic index fiber with the hyperbolic, Gaussian, exponential, and linear profiles are discussed. Results obtained in this study will be of certain potential application on construction of the nonlinear optical devices by soliton control. Results obtained in this study will be of certain value to the studies on the propagation and application of the soliton in the tapered parabolic index fiber and dispersion-managed fiber system.     

On the elastodynamic solution of frictional contact problems using variational inequalities

This article is concerned with the development, implementation and application of variational inequalities to treat the general elastodynamic contact problem. The solution strategy is based upon the iterative use of two subproblems. Quadratic programming and Lagrange multipliers are used to solve the respective first and second subproblems and to identify the candidate contact surface and contact stresses. This approach guarantees the imposition of the active kinematic contact constraints, avoids the use of special contact elements and the interference of the user in dictating the accuracy of the solution. A modified Newmark formulation is developed to integrate the resulting time‐dependent variational inequality. This newly devised implicit time integration scheme is unconditionally stable, second‐order accurate, avoids numerical oscillations present in the traditional Newmark method, and does not cause numerical dissipation. To demonstrate the versatility and accuracy of the newly proposed algorithm, several examples are examined and compared with existing solutions where the penalty method has been employed. Copyright © 2001 John Wiley & Sons, Ltd.     

Multi-hump holographic solitons in photorefractive crystals

We find a novel kind of holographic soliton in a Hamiltonian system, which is described by two arbitrary-amplitude components. Various forms of such types of holographic solitons, not only two- but also multi-hump solitons, can be available. Additionally, we find this new type of holographic soliton can act as a bridge to connect the other types of holographic solitons presented previously.     

Non-collinear magnetism and exchange couplings in FeCo/Mn superlattices

We present the main results of a systematic study of the magnetic properties of Fe_xCo_{1 − x}/Mn_n for various Fe concentrations x and Mn thicknesses n. We show that the magnetic order in the Mn spacer changes from collinear to non-collinear when the Fe concentration decreases. This behaviour is discussed in relation with a bulk ‘canted’ magnetic state nearly degenerate with the collinear AF order. The origin of the exchange of stability between these two magnetic states is ascribed to a stronger collinear character of the Fe/Mn interface than the Co/Mn one.     

Temperature effects on (1+1)-dimensional steady-state bright spatial solitons in biased photorefractive crystals with both the linear and quadratic effects

Abstract

The temperature effects on the intensity profile, self-deflection process, and stability of (1 + 1)-dimensional steady-state bright solitons resulting from both the linear and quadratic electro-optic effects are comprehensively analyzed. Moreover, three physical factors, i.e. diffusion effect, dark irradiance, and the dielectric constant, have been investigated through the theoretical analysis to determine which one dominates the temperature dependence of intensity profile and self-deflection of bright solitons. It is also found that the incident beam evolves into stable bright solitons in the vicinity of initial temperature, but oscillates or even collapses when the crystal temperature deviates significantly from the initial temperature.     

Exhibition of subluminal solitons in a four-level atomic system with two-folded levels

With one weak probe, one strong pumping and one control field, the group velocity dispersion can be balanced by the Kerr effects in a lifetime-broadened four-level atomic medium with two folded levels with proper parameters. This results from the subluminal optical solitons that are formed. Additionally, the conditions for which subluminal solitons occur are given.     

A novel acceleration method for the variational boundary element approach based on multipole expansion

The acoustic radiation of general structures with Neumann's boundary condition using Variational Boundary Element Method (VBEM) is considered. The classical numerical implementation of the VBEM suffers from the computation cost associated with double surface integration. To alleviate this limitation, a novel acceleration method is proposed. The method is based on the expansion of the cross influence matrices in terms of multipoles using the expansion of the Green's function in terms of spherical Bessel functions. Since the resulting multipoles are not dependent on the elements locations, large computation time savings are achieved. Moreover, it is shown that by accounting for the monopole, dipole and quadrupole terms in the multipole expansion, the classical convergence criteria usually used in boundary element guarantee convergence of the proposed method. Several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method. © 1998 John Wiley & Sons, Ltd.     

A quasi-linear technique applied to the method of fundamental solution

This paper proposes the use of a quasi-linear technique for the method of fundamental solution (MFS) to treat the non-linear Poisson-type equations. The MFS, which is a fully meshless method, often deals with the linear and non-linear poisson equations by approximating a particular solution via employing radial basis functions (RBFs). The interpolation in terms of RBFs often leads to a badly conditioned problem which demands special cares. The current work suggests a linearization scheme for the non-homogeneous term in terms of the dependent variable resulting in Helmholtz-type equations whose fundamental solutions are available. Consequently, the MFS can be directly applied to the new linearized equation. The numerical examples illustrate the effectiveness of the presented method.     

Convergence of asynchronous variational integrators in linear elastodynamics

Within the setting of linear elastodynamics of simple bodies, we prove that the discrete action functional obtained by following the scheme of asynchronous variational integrators converges in time. The convergence in space is assured by standard arguments when the finite element mesh is progressively refined. Our strategy exploits directly the action functional. In particular, we show that, if the asynchronicity of time steps and nodal initial data satisfy a boundedness condition, any sequence of stationary points of the discrete action functional is pre‐compact in the weak?* W^1,∞ topology and all its cluster points are stationary points for the continuous (in time) action. In this sense our proof is new with respect to existing ones. Copyright © 2007 John Wiley & Sons, Ltd.     

A reduced basis method for parametrized variational inequalities applied to contact mechanics

We investigate new developments of the reduced-basis method for parametrized optimization problems with nonlinear constraints. We propose a reduced-basis scheme in a saddle-point form combined with the Empirical Interpolation Method to deal with the nonlinear constraint. In this setting, a primal reduced-basis is needed for the primal solution and a dual one is needed for the Lagrange multipliers. We suggest to construct the latter using a cone-projected greedy algorithm that conserves the non-negativity of the dual basis vectors. The reduction strategy is applied to elastic frictionless contact problems including the possibility of using nonmatching meshes. The numerical examples confirm the efficiency of the reduction strategy.     

A variational multiscale method to model crack propagation at finite strains

This contribution presents a hierarchical variational multiscale framework to model propagating discontinuities at finite strains. Thereby the deformation map is decomposed into coarse‐scale and fine‐scale displacements, which results in a decoupled system of coarse‐scale and fine‐scale equations. Both are solved numerically by means of the finite element method whereby crack propagation is taken into account at the fine scale. Growing cracks are numerically handled by the introduction of discontinuous elements. A locality assumption on the fine‐scale solution and an adaptive scheme to resize the fine‐scale domain are introduced and demonstrated to increase the efficiency of the method. Copyright © 2009 John Wiley & Sons, Ltd.