Diverse chirped optical solitons and new complex traveling waves in nonlinear optical fibers

This paper studies chirped optical solitons in nonlinear optical fibers. However, we obtain diverse soliton solutions and new chirped bright and dark solitons, trigonometric function solutions and rational solutions by adopting two formal integration methods. The obtained results take into account the different conditions set on the parameters of the nonlinear ordinary differential equation of the new extended direct algebraic equation method. These results are more general compared to Hadi et al(2018 Optik 172 545–53) and Yakada et al(2019 Optik197 163108).     

Initial-Value Problem of a Coupled Dispersionless System: Dynamical System Approach

We investigate the dynamical behaviour of a coupled dispersionless system （CDS） by solving its initial-value problem following a dynamical system approach. As a result, we unearth a typical miscellaneous travelling waves including the localized and periodic ones. We also investigate the energy density of such waves and find that under some boundary conditions, the localized waves moving towards positive direction are more stable than the periodic waves which on contrary stand for the most conditions. stable travelling waves in another situation of boundary conditions.     

Dynamical System Approach to a Coupled Dispersionless System: Localized and Periodic Traveling Waves

We investigate the dynamical behavior of a coupled dispersionless system describing a current-conducting string with infinite length within a magnetic field. Thus, following a dynamical system approach, we unwrap typical miscellaneous traveling waves including localized and periodic ones. Studying the relative stabilities of such structures through their energy densities, we find that under some boundary conditions, localized waves moving in positive directions are more stable than periodic waves which in contrast stand for the most stable traveling waves in another boundary condition situation.     

Exact traveling wave solutions to the fourth‐order dispersive nonlinear Schrödinger equation with dual‐power law nonlinearity

In this paper, we investigate exact traveling wave solutions of the fourth‐order nonlinear Schrödinger equation with dual‐power law nonlinearity through Kudryashov method and (G'/G)‐expansion method. We obtain miscellaneous traveling waves including kink, antikink, and breather solutions. These solutions may be useful in the explanation and understanding of physical behavior of the wave propagation in a highly dispersive optical medium. Copyright © 2015 John Wiley & Sons, Ltd.     

Intramolecular catalysis and the rate-determining step in the alkaline hydrolysis of ethyl salicylate

The alkaline hydrolysis of ethyl salicylate has been studied at 35°C within the [ōH] range of 0.001–2.00 M. The observed hydroxide ion concentration dependence of rate has been explained by proposing the occurrence of two parallel kinetic steps shown as in the rate law: rate = k₁[H₂O] [ES ] + k₂[ōH] [ES ] where ES^? represents ionized ethyl salicylate. The value of k₁, is ca. 10⁶ times larger than the expected value of rate constant for uncatalyzed aqueous cleavage of ethyl-p-hydroxybenzoate. This rate advantage is attributed to intramolecular general base catalysis. The analysis of observed activation parameters indicates that ca. 10⁶ times rate enhancement is entirely due to favorable entropy change. The Brønsted-type plots show an extremely low sensitivity of rate constants k₁ and k₂ with respective Brønsted coefficient of β = ?0.03 ± 0.01 and β = ?0.01 ± 0.05, on the basicity of leaving groups of salicylate esters (alkoxide and phenoxide ions). The low values of these Brønsted coefficients indicate essentially little or an insignificant amount of bond cleavage between carbonyl carbon and leaving group in the rate-determining step in both the k₁ and k₂ steps. The rate constants obtained at different ethanol concentration follow Grunwald-Winstein mY equation with m = 0.14 ± 0.01.     

Optical chirped soliton in metamaterials

We present the iterative classical point symmetry analysis of a shallow water wave equation in \(2+1\) dimensions and that of its corresponding nonisospectral, two-component Lax pair. A few reductions arise and are identified with celebrate equations in the Physics and Mathematics literature of nonlinear waves. We pay particular attention to the isospectral or nonisospectral nature of the reduced spectral problems.     

Chaos in semiconductor band-trap impact ionization

We introduce a new spatially-extended semiconductor carriers transport equation model, based on generation–recombination process of the band-trap impact ionization under a longitudinal electric field. By means of numerical studies, we demonstrate the existence of chaos. Also, we present many results such as, the lyapunov spectrum, the bifurcation diagram, the phase portrait and the Poincaré surface of section. In addition the basic electric circuit used is found to be helpful in the implementation of a simple and autonomous chaotic oscillator circuit. Furthermore, the obtained results are interesting in the way that they could be useful in avoiding of undesirable chaotic regime in some switching and memory electronic devices.     

Miscellaneous Rotating Solitary Waves to a Coupled Dispersionless System

We investigate the soliton structure of a coupled dispersionless system describing a current-conducting string with infinite length within a magnetic field. Thus, following Hirota＇s method, we unwrap three typical localized waves with nonzero angular momentum depending strongly upon their angular velocities. Illustrating the soliton behavior of these waves, we focus our interests on breather-like waves and depict the elastic scattering amongst such waves.     

Dynamical survey of a generalized-Zakharov equation and its exact travelling wave solutions

We investigate the dynamical behavior of a generalized-Zakharov equation for the complex envelope of the high-frequency wave and the real low-frequency field by analyzing its phase portraits. Following a dynamical system approach, in different parameter regions, we depict phase portraits of a travelling wave system. Through discussing the bifurcation of phase portraits, we unwrap explicit miscellaneous travelling waves including localized and periodic ones.     

On Periodic Wave Solutions to (1+1)-Dimensional Nonlinear Physical Models Using the Sine-Cosine Method

We investigate two interesting (1+1)-dimensional nonlinear partial differential evolution equations (NLPDEEs), namely the nonlinear dispersion equation with compact structures and the generalized Camassa–Holm (CH) equation describing the propagation of unidirectional shallow water waves on a flat bottom, and arising in the study of a certain non-Newtonian fluid. Using an interesting technique known as the sine-cosine method for investigating travelling wave solutions to NLPDEEs, we construct many new families of wave solutions to the previous NLPDEEs, amongst which the periodic waves, enriching the wide class of solutions to the above equations.