Evolution of solitary waves for a perturbed nonlinear Schrödinger equation

Soliton perturbation theory is used to determine the evolution of a solitary wave described by a perturbed nonlinear Schrödinger equation. Perturbation terms, which model wide classes of physically relevant perturbations, are considered. An analytical solution is found for the first-order correction of the evolving solitary wave. This solution for the solitary wave tail is in integral form and an explicit expression is found, for large time. Singularity theory, usually used for combustion problems, is applied to the large time expression for the solitary wave tail. Analytical results are obtained, such as the parameter regions in which qualitatively different types of solitary wave tails occur, the location of zeros and the location and amplitude of peaks, in the solitary wave tail. Two examples, the near-continuum limit of a discrete NLS equation and an explicit numerical scheme for the NLS equation, are considered in detail. For the discrete NLS equation it is found that three qualitatively different types of solitary wave tail can occur, while for the explicit finite-difference scheme, only one type of solitary wave tail occurs. An excellent comparison between the perturbation solution and numerical simulations, for the solitary wave tail, is found for both examples.     

Ligandless C‐C bond formation via Suzuki–Miyaura reaction in micelles or water–ethanol solution using PdPtZn and PdZn nanoparticle thin films

PdPtZn and PdZn nanoparticle (NP) thin films were synthesized by the reduction of [PdCl₂(cod)], [PtCl₂(cod)] (cod = cis,cis‐1,5‐cyclooctadiene) and [Zn(acac)₂] (acac = acetylacetonate) complexes at an oil–water interface. The structure and morphology of the as‐prepared NPs were characterized with X‐ray diffraction, transmission electron microscopy and energy dispersive analysis of X‐rays. Catalytic activity of the prepared NPs was investigated in the Suzuki–Miyaura cross‐coupling reaction in H₂O–EtOH and various micellar media systems such as cetyltrimethylammonium bromide (cationic surfactant), sodium dodecylsulfate (anionic surfactant) and Pluronic P123 (non‐ionic surfactant). PdPtZn and PdZn thin films exhibited higher catalytic activity compared to Pd thin film in the Suzuki–Miyaura coupling reaction due to the appropriate interaction between palladium, platinum and zinc metals. Copyright © 2015 John Wiley & Sons, Ltd.     

Synthesis of Core-Shell Magnetic Supramolecular Nanocatalysts based on Amino-Functionalized Calix[4]arenes for the Synthesis of 4H-Chromenes by Ultrasonic Waves

One of the most common phenol-formaldehyde cyclic oligomers from hydroxyalkylation reactions that exhibit supramolecular chemistry are calixarenes. These macrocyclic compounds are qualified to act as synthetic catalysts due to their specific features including being able to form host-guest complexes, having unique structural scaffolds and their relative ease of chemical modifications with a variety of functions on their upper rim and lower rim. Here, a functional magnetic nanocatalyst was designed and synthesized by using a synthetic amino-functionalized calix[4]arene. Its catalytic activity was evaluated in a one-pot synthesis of 2-amino-4H-chromene derivatives. Besides, this novel magnetic nanocatalyst was characterized by spectroscopic and analytical techniques such as FT-IR, EDX, FE-SEM, TEM VSM, XRD analysis.     

Epoxidation of 1,4-Diaroyl Ethene Derivatives in the Presence of UHP or H2O2

Hydrogen peroxide (H₂O₂) or urea–hydrogen peroxide (UHP) in basic media react with carbon–carbon double bonds of 1,4-diaroyl ethenes to produce the corresponding epoxides.     

Meglumine sulfate catalyzed solvent-free one-pot synthesis of coumarins under microwave and thermal conditions

A convenient method has been developed for the Pechmann reaction of phenols and β-keto esters catalyzed by meglumine sulfate. Solvent-free conditions, inexpensive catalyst, short reaction times, high yield, and ease of purification of the products are the advantages of this protocol. This novel catalytic system is expected to contribute to the development of more benign Pechmann condensation reactions of phenols with β-keto esters.     

Understanding the high temperature oxidation and ignition behaviour of two-phase Mg–Nd alloys and a comparison to single phase Mg–Nd

The oxidation kinetics and the mechanism of two-phase Mg–Nd alloys were investigated via isothermal heating experiments conducted in dry air at 500 °C for 12 h. The oxidation kinetic curves reveal improved oxidation resistance on neodymium (Nd)-containing alloys compared to pure Mg. A lower mass gain was detected at 2.5-%Nd than at 6-Nd%, which was related to the lower amount of intermetallic phase on the alloy surface. The intermetallic phase has a significant effect on the oxide growth stage. Nd₂O₃ formation on the intermetallic phases creates diffusion paths for oxygen to the metal/oxide interface, affecting both the oxidation kinetics and the oxidation resistance of the alloys. The formation of a Nd-depleted region at the subsurface due to extensive Nd oxidation at the oxide/intermetallic interface lowers the protective ability of the oxide scale. As increasing the Nd content of binary Mg–Nd alloys above 0.5 wt% shifts the alloys from single-phase region to two-phase region, it adversely affects the ignition resistance.     

A pseudospectral method for nonlinear Duffing equation involving both integral and non‐integral forcing terms

The Legendre pseudospectral method is developed for the numerical solution of nonlinear Duffing equation involving both integral and non‐integral forcing terms. By using differentiation matrix, the problem is reduced to the solution of a system of algebraic equations. The method is general, easy to implement, and yields very accurate results. Numerical experiments are presented to demonstrate the accuracy and the efficiency of the proposed computational procedure. Copyright © 2014 John Wiley & Sons, Ltd.