Conservation laws for a complexly coupled KdV system,coupled Burgers’ system and Drinfeld–Sokolov–Wilson system via multiplier approach

The multiplier approach (variational derivative method) is used to derive the conservation laws for some nonlinear systems of partial differential equations. Firstly, the multipliers (characteristics) are computed and then conserved vectors are obtained for the each multiplier. Examples of the third-order complexly coupled KdV system, second-order coupled Burgers’ system and third-order Drinfeld–Sokolov–Wilson system are considered. For all three systems the local conservation laws are established by utilizing the multiplier approach.     

New soliton and periodic solutions of (1 + 2)-dimensional nonlinear Schrödinger equation with dual-power law nonlinearity

With the aid of symbolic computation, the new generalized algebraic method is extended to the (1 + 2)-dimensional nonlinear Schrödinger equation (NLSE) with dual-power law nonlinearity for constructing a series of new exact solutions. Because of the dual-power law nonlinearity, the equation cannot be directly dealt with by the method and require some kinds of techniques. By means of two proper transformations, we reduce the NLSE to an ordinary differential equation that is easy to solve and find a rich variety of new exact solutions for the equation, which include soliton solutions, combined soliton solutions, triangular periodic solutions and rational function solutions. Numerical simulations are given for a solitary wave solution to illustrate the time evolution of the solitary creation. Finally, conditional stability of the solution in Lyapunov’s sense is discussed.     

Optical solitons with non-Kerr law nonlinearity and inter-modal dispersion with time-dependent coefficients

This paper studies optical solitons with non-Kerr law nonlinearity, in the presence of inter-modal dispersion. The coefficients of group velocity dispersion, nonlinearity and inter-modal dispersion terms have time-dependent coefficients. The types of nonlinearity that are considered are Kerr, power, parabolic and dual-power laws. The solitary wave ansatz is used to carry out the integration of the governing nonlinear Schrödinger’s equation with time-dependent coefficients. Both, bright and dark optical solitons, are considered, in this paper. Finally, numerical simulations are also given in each of these cases. The only necessary condition for these solitons to exist is that these time-dependent coefficients of group velocity dispersion and inter-modal dispersion are Riemann integrable.     

Free vibration analysis of linear particle chain impact damper

Impact dampers have gained much research interest over the past decades that resulted in several analytical and experimental studies being conducted in that area. The main emphasis of such research was on developing and enhancing these popular passive control devices with an objective of decreasing the three parameters of contact forces, accelerations, and noise levels. To that end, the authors of this paper have developed a novel impact damper, called the Linear Particle Chain (LPC) impact damper, which mainly consists of a linear chain of spherical balls of varying sizes. The LPC impact damper was designed utilizing the kinetic energy of the primary system through placing, in the chain arrangement, a small-sized ball between each two large-sized balls. The concept of the LPC impact damper revolves around causing the small-sized ball to collide multiple times with the larger ones upon exciting the primary system. This action is believed to lead to the dissipation of part of the kinetic energy at each collision with the large balls.     

Synchronization criteria in complex dynamical networks with nonsymmetric coupling and multiple time-varying delays

In this article, we consider a generalized complex dynamical network model with nonsymmetric coupling, and the dynamics of each node has a different time-varying delay. Criteria of exponential synchronization are derived in terms of linear matrix inequalities for the model by constructing suitable Lyapunov functionals. The obtained outcomes are different from those in the current literature, in which the complex dynamical networks are coupling symmetrically and delays are fixed constants. Moreover, the given sufficient conditions extend current available results and are verifiable. A numerical example is provided to illustrate the efficiency of the derived outcome.     

Temperature-dependent photovoltaic behavior of CdSe quantum dots/P3HT hybrid thinfilm

An organic–inorganic hybrid solar cell based on CdSe quantum dots (QDs) and poly(3-hexylthiophene) (P3HT) was fabricated. Its temperature-dependent photovoltaic behaviors, such as I–V characteristic curves and open circuit voltage (V_oc) transient response, were measured. The photovoltaic behavior of this hybrid thin film device was similar with that of organic thin film solar cells, according to analysis results based on the equivalent circuit method. The exact carrier lifetime was remarkably different between under low-temperature region and under temperature above 197 K.     

Spin waves transport across a ferrimagnetically ordered nanojunction of cobalt-gadolinium alloy between cobalt leads

A model calculation is presented for the spin wave scattering and coherent transport at the ferrimagnetically ordered cobalt-gadolinium alloy nanojunction between cobalt leads. The structural model for the amorphous alloy nanojunction [Co_1/2Gd_1/2]₃ is considered as an ordered alloy hcp structure of three (0001) atomic planes between the leads. To analyze the spin dynamics and spin wave scattering at the nanojunction boundary, the phase field matching method (PFMT) is implemented over the ground state of the system, in the Heisenberg Hamiltonian representation. The coherent reflection and transmission probabilities of spin waves from the cobalt leads incident onto the nanojunction boundary are calculated, and numerical results are presented for the coherent SW transport across the nanojunction over the entire range of their frequencies. The results are especially valid in the interval between nanometric SW wavelengths greater than the nanojunction width and macroscopic wavelengths. They demonstrate in particular, the possibility of the resonance assisted maxima for the SW transmission spectra owing to the interactions between the incident spin waves and the localized spin resonances on the nanojunction. This effect is general and may be observed at different characteristic frequencies and corresponding incident angles.     

A branch-and-price algorithm for the two-stage guillotine cutting stock problem

We investigate the two-stage guillotine two-dimensional cutting stock problem. This problem commonly arises in the industry when small rectangular items need to be cut out of large stock sheets. We propose an integer programming formulation that extends the well-known Gilmore and Gomory model by explicitly considering solutions that are obtained by both slitting some stock sheets down their widths and others down their heights. To solve this model, we propose an exact branch-and-price algorithm. To the best of our knowledge, this is the first contribution with regard to obtaining integer optimal solutions to Gilmore and Gomory model. Extensive results, on a set of real-world problems, indicate that the proposed algorithm delivers optimal solutions for instances with up to 809 items and that the hybrid cutting strategy often yields improved solutions. Furthermore, our computational study reveals that the proposed modelling and algorithmic strategy outperforms a recently proposed arc-flow model-based solution strategy.     

Optical solitons due to quadratic nonlinearities: from basic physics to futuristic applications

We present an overview of nonlinear phenomena related to optical quadratic solitons—intrinsically multi-component localized states of light, which can exist in media without inversion symmetry at the molecular level. Starting with presentation of a few derivation schemes of basic equations describing three-wave parametric wave mixing in diffractive and/or dispersive quadratic media, we discuss their continuous wave solutions and modulational instability phenomena, and then move to the classification and stability analysis of the parametric solitary waves. Not limiting ourselves to the simplest spatial and temporal quadratic solitons we also overview results related to the spatio-temporal solitons (light bullets), higher order quadratic solitons, solitons due to competing nonlinearities, dark solitons, gap solitons, cavity solitons and vortices. Special attention is paid to a comprehensive discussion of the recent experimental demonstrations of the parametric solitons including their interactions and switching. We also discuss connections of quadratic solitons with other types of solitons in optics and their interdisciplinary significance.