Bright solitons of the variants of the Novikov–Veselov equation with constant and variable coefficients

In this paper, the existence of the bright soliton solution of four variants of the Novikov–Veselov equation with constant and time varying coefficients will be studied. We analyze the solitary wave solutions of the Novikov–Veselov equation in the cases of constant coefficients, time-dependent coefficients and damping term, generalized form, and in 1 + N dimensions with variable coefficients and forcing term. We use the solitary wave ansatz method to derive these solutions. The physical parameters in the soliton solutions are obtained as functions of the dependent coefficients. Parametric conditions for the existence of the exact solutions are given. The solitary wave ansatz method presents a wider applicability for handling nonlinear wave equations.     

α-Na3M2(PO4)3 (M = Ti, Fe): absolute cationic ordering in NASICON-type phases

The structure of the fully ordered α-Na(3)Ti(2)(PO(4))(3) NASICON compound was elucidated using high-quality single-crystal data. The cation/vacancy distribution forms a homogeneous 3D arrangement and could represent the absolute cationic ordering available in the full Na(3)M(2)(PO(4))(3) series, as verified for M = Fe. For M = Ti, the reversible α → γ transition was observed at 85 °C, leading to the standard disordered R ?3c γ model. Through JPDF analysis, the most probable Na(+) zigzag M(2)-M(1) diffusion scheme was directly deduced using our accurate crystallographic data.     

A study of shallow water waves with Gardner’s equation

In this paper the dynamics of solitary waves governed by Gardner’s equation for shallow water waves is studied. The mapping method is employed to carry out the integration of the equation. Subsequently, the perturbed Gardner equation is studied, and the fixed point of the soliton width is obtained. This fixed point is then classified. The integration of the perturbed Gardner equation is also carried out with the aid of He’s semi-inverse variational principle. Finally, Gardner’s equation with full nonlinearity is solved with the aid of the solitary wave ansatz method.     

Chemical compounds from Phoenician juniper berries (Juniperus phoenicea)

Natural chemical compounds are a widely researched topic worldwide because of their potential activity against cerebrovascular diseases. Chemicals from Juniperus phoenicea berries are reported in this study. Lipids (11%) from seeds are mainly unsaturated (86%). Minerals are also quantified like Na (63.8?mg per 100?g?DW) or K (373.9?mg per 100?g?DW). Total reduced sugars are ca 192.6?mg?g(-1)?DW. Polyphenols and flavonoids from berries are highly present with an average of 1764?±?174.3?mg gallic acid per 100?g?DW and 890?±?47.6?mg rutin per 100?g?DW, respectively. Mean free radical scavenging activities, determined by DPPH and ABTS, are 1337?±?126.2?mM TEAC per 100?g?DW and 1105.7?±?95.9?mM TEAC per 100?g?DW, respectively. All findings improve the possible presence of biologically active fractions in phytocomplex that could be used as such and/or extracted for the formulation of supplements and/or ingredients for the pharmaceutical industry.     

Solitary wave and shock wave solutions to a second order wave equation of Korteweg-de Vries type

This paper obtains the solitary wave as well as the shock wave solutions to the second order wave equation of Korteweg-de Vries type that was first proposed in 2002. The ansatz method is used to retrieve these solutions. The domain restrictions as well as the parameter regimes are all identified in the process of obtaining the solution.     

Dark optical solitons and conservation laws for parabolic and dual-power law nonlinearities in (2 + 1)-dimensions

This paper studies the dynamics of optical solitons with parabolic and dual-power law nonlinearities. The dark 1-soliton solution is first obtained by the ansatz method along with the necessary constraint conditions, for both of these nonlinearities. Subsequently, the invariance, conservation laws and double reductions of the governing nonlinear Schrödinger's equation are studied and the conserved densities are thus revealed.     

Ruthenium catalysts supported on TiO<Subscript>2</Subscript> prepared by sol–gel way for <Emphasis Type="Italic">p</Emphasis>-hydroxybenzoic acid wet air oxidation

The wet air oxidation of p-hydroxybenzoic acid, chosen as a model compound of olive mills wastewaters was carried out at 140 °C and 50 bar air over Ru catalysts supported on TiO₂ prepared by sol–gel method. These catalysts were characterized by means of N₂ adsorption–desorption, XRD and TEM. Optimization of the catalytic performances was obtained by studying some parameters such as the catalyst preparation method, the solvent evacuation way, the nature of the hydrolysis agent, the influence of the ruthenium salt used as the metal precursor (Ru(NO)(NO₃)₃ or Ru(acac)₃) and the catalyst pretreatment. The pre-calcination of the catalyst precursor at 300 °C under oxygen, before the reduction step under hydrogen, was detrimental to the activity. The results showed that the use of nitric acid as hydrolysis agent, drying under supercritical conditions and the use of Ru(NO)(NO₃)₃ leads to the more efficient catalyst with high TOC abatement.