一类5阶KdV方程的孤立波解

近年来,关于3阶KdV方程的孤立波解得到迅速发展,而对于5阶KdV方程的孤立波解文献报道较少.本文主要采用Sine-Cosine展开法得到了一类5阶KdV方程的孤立波解;然后利用Matlab计算软件,获得了孤立波解的图形,其结果展示了孤立子与系数之间的相互关系;最后,应用所得的结果分别得到了Lax方程, SK方程, CDG方程的孤立波解.     

Burgers-Huxley方程的同伦分析解

针对Burgers-Huxley方程定解问题,构造了一种零阶同伦方程,采用同伦方法得到Burgers-Huxley方程定解问题的近似解析解.最后,进行了实例验证和结果分析.     

浅水波方程和Klein-Gordon方程新的精确行波解

采用了一种新的方法来求解浅水波方程和Klein-Gordon的行波解.在该方法下,Klein-Gordon方程和浅水波方程都得到了其精确的周期孤立波解,从而该方法的有效性得到了验证.     

抽象泛函微分方程—整体解的存在性与稳定性

本文在一次近似方程的解具有指数衰减性质的条件下,采用逐步逼近方法得到了原方程整体解的存在唯一性和稳定性结果.     

非线性发展方程新的显式精确解

借助Ｍａｔｈｅｍａｔｉｃａ系统,采用三角函数法和吴文俊消元法,本文获得了著名的２＋１维ＫＰ方程的若干精确解,其中包括新的精确解和孤波解．在此基础上,进而得到著名ＫｄＶ方程、Ｈｉｒｏｔａ－Ｓａｔｓｕｍａ方程和耦合ＫｄＶ方程的一些精确解．     

（2＋1）维KP方程的三类精确解

研究了（2＋1）维KP方程的孤子解问题．应用Riccati方程映射法,得到了（2＋1）维KP方程的新的显式精确解的结构．根据得到的精确解结构,构造出了该方程的三类精确解．     

应用改进的简单方程法求非线性数学物理方程的精确解

应用改进的简单方程法求得Cahn-Allen方程和Jimbo-Miwa方程的精确解,这些解包括双曲函数解、三角函数解.当对双曲函数解中的参数取特殊值时,可以得到了孤立波解.当对三角函数解中的参数取特殊值时,可以得到对应的周期波函数解.实践证明,简单方程法对于研究非线性数学物理方程具有非常广泛的应用意义.     

同伦分析法求解Burgers方程的初边值问题

采用同伦分析法求解了Burgers方程的一初边值问题,得到了它的近似解析解.在不同粘性系数情形下,对近似解与精确解进行了比较,发现在粘性系数不是非常小的情况下,用此方法得到的解析解与精确解符合地很好.     

板弯曲问题的具两组高阶基本解序列的MRM方法

讨论了双参数地基上薄板弯曲问题.利用两组高阶基本解序列,即调和及重调和基本解序列,采用多重替换方法(MRM方法),得到了板弯曲问题的MRM边界积分方程.证明了该方程与边值问题的常规边界积分方程是一致的.因此由常规边界积分方程的误差估计即可得到板弯曲问题MRM方法的收敛性分析.此外该方法还可推广到具多组高阶基本解序列的情形.     

Gardner-Kadomtsev-Petviashvili方程的精确行波解与分支

本文讨论Gardner-Kadomtsev-Petviashvili方程的行波解,该方程在物理中有广泛应用.我们运用动力系统分支理论,首先得到了方程的分支和相图,然后通过讨论参数的范围得到了精确行波解的所有形式,其中包括孤波解,周期波解,扭波解和爆破解     

Dark spatial soliton interaction in nonlinear Kerr medium

The dark spatial soliton interaction in nonlinear Kerr medium has been studied in this paper. The problem has been solved by the use of the slowly varying envelope approximation in solving coupled nonlinear Schrödinger equations. The perturbation nature of dark spatial soliton interaction has been described and some of their key properties has been discussed as well in the paper.     

Spectra and ionization potential of cyanoacetylene

The spectrum of cyanoacetylene has been photographed in the vacuum ultraviolet region and its analysis made. The ionization potential has been calculated from an observed Rydberg series to be 11.6 eV. The first Rydberg band has been compared with the photoelectron spectrum of the molecule and conclusions about the initial orbital have been drawn.     

Fuzzy periodic review system with fuzzy random variable demand

In this paper, a periodic review inventory system has been analyzed in a mixed imprecise and uncertain environment where fuzziness and randomness appear simultaneously. A model has been developed with customer demand assumed to be a fuzzy random variable. The lead-time has been assumed to be a constant. The lead-time demand and the lead-time plus one period’s demand have also been assumed to be fuzzy random variables. A methodology has been developed to determine the optimal inventory level and the optimal period of review such that the total expected annual cost in the fuzzy sense is minimized. A numerical example has been presented to illustrate the model.     

Effect of change point and imperfect debugging in software reliability and its optimal release policy

This article presents a software reliability growth model based on non-homogeneous Poisson process. The main focus of this article is to deliver a method for software reliability modelling incorporating the concept of time-dependent fault introduction and fault removal rate with change point. Also in this article, a cost model with change point has been developed. Based on the cost model optimal release policy with change point has been discussed. Maximum likelihood technique has been applied to estimate the parameters of the model. The proposed model has been validated using some real software failure data. Comparison has been made with models incorporating change point and without change point. The application of the proposed cost model has been shown using some numerical examples.     

FREE SOLVABLE P-ALGEBRAS

The construction of a free solvable P-algebra of finite degree k in the variety of all solvable P-algebras of degree at most k (k ≥ 1) has been given. Some properties of the same have been studied. The structure of the free solvable P-algebra has been viewed as a module over a ring with several objects. The Magnus embedding theorem associated with the Fox-derivative in a free group ring has been considered to prove properties associated with the partial (Fox) derivative in a free associative ring. Residual nilpotency and triviality of the center of a free metabelian P-algebra has been proved. Various properties of a homomorphism associated with a free metabelian P-algebra of finite rank have been studied. The non-embedding property of a free solvable P-algebra of degree k of higher rank in a lower rank has also been presented here.     

Solvent extraction studies of indium

Solvent extraction of indium from malonic acid medium by Primene JM-T has been studied. The extraction has been studied as a function of pH and concentrations of malonic acid and sodium malonate. The nature of the acid-amine complex has been established by chemical analysis and by the application of the method of Hogfeldt and Fredlund. The equilibrium constant for the reaction has also been calculated. The nature of the indium complexes getting extracted has also been discussed.     

Terminal motion of a thin elliptical plate over a horizontal plane with orthotropic friction

The problem on the terminal motion of a thin elliptic plate over a horizontal plane taking into account orthotropic friction forces has been considered. Differential equations of the movement of the plate have been derived. The system of equations has been numerically solved under various initial conditions. It has been shown that sliding and spinning cease simultaneously. It has been found that the limiting behavior of the plate is governed not only by the ratio of the moment of inertia to the coefficient of friction, but also by the orientation of the plate. A comparison of the behaviors of the elliptic and circular plates has been carried out. The results of the calculations can be used to describe the phenomena that occur in a rail–wheel contact in more detail.     

Free vibrations and stability of hydraulic cylinder fixed elastically on both ends

The boundary value problem of the stability and free vibration of a hydraulic cylinder has been formulated and solved in this paper. The considered hydraulic cylinder has been elastically fixed at both ends and loaded by Euler force. An elastical fixation has been modelled by rotational springs. The mentioned above hydraulic cylinder consists of a piston rod and cylinder replaced by rods. There are conditions of continuity between the rods. The boundary value problem has been formulated on the basis of minimum potential energy (static problem) and on the basis of Hamilton's principle (free vibration problem). In this paper example results of numerical calculations of the stability and free vibration have been presented. Experimental research has been performed in order to verify the correctness of the assumed mathematical model. Professional measuring apparatus and special stand for research into the slender systems have been used in experiment. Natural frequencies have been measured in dependence on the values of an external load. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dirichlet Problem for a Fractional-Order Ordinary Differential Equation with Retarded Argument

A solution of the Dirichlet problem for a fractional-order ordinary differential equation has been found. Green’s function has been constructed for the problem concerned. The problem solution has been written in terms of Green’s function. A theorem on the existence and uniqueness of a solution of the posed problem has been proved, and a condition for its unique solvability has been derived. It is shown that the condition of solvability may only be violated a finite number of times.     

Love waves in a fluid-saturated porous layer under a rigid boundary and lying over an elastic half-space under gravity

In this paper, mathematical modeling of the propagation of Love waves in a fluid-saturated porous layer under a rigid boundary and lying over an elastic half-space under gravity has been considered. The equations of motion have been formulated separately for different media under suitable boundary conditions at the interface of porous layer, elastic half-space under gravity and rigid layer. Following Biot, the frequency equation has been derived which contain Whittaker’s function and its derivative that have been expanded asymptotically up to second term (for approximate result) for large argument due to small values of Biot’s gravity parameter (varying from 0 to 1). The effect of porosity and gravity of the layers in the propagation of Love waves has been studied. The effect of hydrostatic initial stress generated due to gravity in the half-space has also been shown in the phase velocity of Love waves. The phase velocity of Love waves for first two modes has been presented graphically. Frequency equations have also been derived for some particular cases, which are in perfect agreement with standard results. Subsequently the lower and upper bounds of Love wave speed have also been discussed.