Symmetry Analysis of Two Types of （2＋1）-Dimensional Nonlinear Klein-Gorden Equation

By means of the classical symmetry method, we investigate two types of the （2＋1）-dimensional nonlinear Klein-Gorden equation. For the wave equation, we give out its symmetry group analysis in detail. For the second type of the （2＋1）-dimensional nonlinear Klein-Gorden equation, an optimal system of its one-dimensional subalgebras is constructed and some corresponding two-dimensional symmetry reductions are obtained.     

Aggregation processes in micellar solutions: a Raman study

Ionic surfactants such as sodium dodecyl sulfate (SDS) belong to the amphiphile family: they possess a long hydrophobic hydrocarbon chain and a polar hydrophilic headgroup. In a polar solvent and over the critical micellar concentration these molecules join to form micelles. The micellar solutions, in turn, if doped with various ligands tend to aggregate. Solid SDS, micelles of SDS in water and micelles of SDS doped with two types of macrocyclic ligands, Kryptofix 2.2.2 (K222) and crown ether 18‐Crown‐6 (18C6), at different concentrations are studied by Raman scattering, that represents a new approach to such systems. The experimental Raman spectrum, obtained on crystalline powders of SDS, is compared with the ab initio computed spectrum in order to assign the vibrational bands. After discriminating sensitive peaks by comparing the crystalline powders of the single components and their water solutions, the aggregation process and the action of the ligands are analyzed following the evolution of the intensity and wavenumber of these characteristic Raman peaks. This shows that Raman spectroscopy is sensitive to the aggregation dynamics and to the effects induced by the hydration layer on the molecules in solutions. A saturation effect in the aggregation process with the increase of the ligand concentration is observed. Copyright © 2012 John Wiley & Sons, Ltd.     

(n+1)维双Sine-Gordon方程的新精确解

给出包含第一种椭圆方程的三角函数型辅助方程及其解的叠加公式.在一般函数变换下,借助符号计算系统Mathematica,构造了(n+1)维双sine-Gordon方程新的Jacobi椭圆函数精确解.这些解包括了行波变换下的Jacobi椭圆函数精确解、精确孤立波解和三角函数解.     

(2+1)维Konopelchenko-Dubrovsky方程新的多孤子解

利用齐次平衡方法,将(2+1)维Konopelchenko-Dubrovsky方程转化为两个变量分离的线性偏微分方程,然后采用三种不同的函数假设,得到相应的常系数微分方程,通过求解特征方程,方便地构造出Konopelchenko-Dubrovsky方程新的多孤子解.     

The constructive technique and its application in solving a nonlinear reaction diffusion equation

A mathematical technique based on the consideration of a nonlinear partial differential equation together with an additional condition in the form of an ordinary differential equation is employed to study a nonlinear reaction diffusion equation which describes a real process in physics and in chemistry. Several exact solutions for the equation are acquired under certain circumstances.     

Travelling solitary wave solutions for the generalized Burgers--Huxley equation with nonlinear terms of any order

In this paper, the travelling wave solutions for the generalized Burgers--Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.     

Rational solutions to Q3δ in the Adler-Bobenko-Suris list and degenerations

We derive rational solutions in Casoratian form for the Nijhoff-Quispel-Capel (NQC) equation by using the lattice potential Korteweg-de Vries (lpKdV) equation and two Miura transformations between the lpKdV and the lattice potential modified KdV (lpmKdV) and the NQC equation. This allows us to present rational solutions for the whole Adler-Bobenko-Suris (ABS) list except Q4. The known Miura transformation for soliton solutions between the NQC equation and Q3_δ and the known degenerations for solitons from Q3_δ to Q2, Q1_δ, H3_δ, H2 and H1 in the ABS list are used. We show that the Miura transformation and degenerations are valid as well for rational solutions which are usually considered as “long-wave-limit” of solitons. All the rational solutions can be expressed in terms of {z _j} which are linear functions of (n, m).     

Untersuchung der spontanen Abscheidung von Silber an pulverförmigem Platin aus salpetersauren Lösungen

Es wurde festgestell, daβ Silberionen an mit wasserstoffgesättigten Platimpulver sich abschieden und die maximal abgeschiedence Menge im Salpeterāure-Konzentrationsbereich 5 n – 0,0001 n die der Monoshcict entsprechende Menge nicht erreicht. Die Meβergebnisse bezüglich der Konzentrationsabhängigkeit der Abscheidung scheinen formell die Langmuirsche Gleichung zu erfūllen, doch zeigen die aus dieser Gleichung berechneten T_σ - Werte eine pH-Abhāngigkeit und stimmen mit der BET-Ober-fläche nicht überein. Die spontne Abscheidung von Silber an Platinpulver kann für die Abtennung von radioaktiven Silber-Isotopen angewandt werden.     

Gamma-Radiolyse von Dimethylglyoxim

Die Strahlenresistenz von reinem und an Aktivkohle sorbiertem Dimethylglyoxim (DMG), das für die selektive Abtrennung von Palladium aus Abfallösungen der Kernbrennstoffwiederaufarbeitung geeignet ist, wurde untersucht. Die Bestrahlung erfolgte bei 20–40 °C mit einer ⁶⁰Co-γ-Bestrahlungsanlage mit Dosisleistungen von 0,6 bis 1,7 Gy/s in einem Dosisbereich von 2 kGy bis 5 MGy. Die Radiolyseprodukte wurden mit verschiedenen Methoden analysiert und die G-werte bestimmt. Es wurde gezeigt, daβ DMG bis zu Dosen von etwa 110 kGy relativ strahlenresistent ist. Bei höheren Dosen werden die reaktiven NOH-Gruppen des DMG teilweise zerstört, so daβ sie nicht mit Palladium reagieren können. In Verfahren zur Abtrennung von Palladium aus radioaktiven Abfallösungen werden diese Dosen jedoch nicht erreicht. Auf eine unzureichende Strahlenresistenz von DMG zurückzuführende Komplikationen können deshalb ausgeschlossen werden.