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| 1 | Abundant Exact Traveling Wave Solutions of Generalized Bretherton Equation via Improved (G′/G)-Expansion Method显示文摘In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves. | M.Ali Akbar Norhashidah Hj.Mohd.Ali E.M.E.Zayed | 2012 | Communications in Theoretical Physics2012，57，2： | 10 |
| 2 | Exact Solutions of Nonlinear Evolution Equations in Mathematical Physics Using the Modified Simple Equation Method显示文摘The modified simple equation method is employed to construct the exact solutions involving parameters of nonlinear evolution equations via the (1+1)-dimensional modified KdV equation,and the (1+1)-dimensional reaction-diffusion equation.When these parameters are taken to be special values,the solitary wave solutions are derived from the exact solutions.It is shown that the proposed method provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. | E.M.E.Zayed S.A.Hoda Ibrahim | 2012 | Chinese Physics Letters2012，29，6： | 10 |
| 3 | THE WAVE EQUATION APPROACH TO THE TWO-DIMENSIONAL INVERSE PROBLEM FOR A GENERAL BOUNDED DOMAIN WITH PIECEWISE SMOOTH MIXED BOUNDARY CONDITIONS显示文摘The spectral distribution exp( ), where {} are the eigenvalues of the negative Laplacian -△=- in the (x^1,x^2)-plane, is studied for a variety of domains, where -∞< t <∞ and i=(1/2)(-1) . The dependence of (t)on the connectivity of a domain and the boundary conditions are analyzed. Particular attention is given to a general bounded domain Ω in R^2 with a smooth boundary Ω, where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the piecewise smooth parts Γj(j = 1,……,n) of Ω are considered such that Some geometrical properties of Ω(e.g., the area of Ω, the total lengths of the boundary, the curvature of its boundary, etc.) are determined, from the asymptotic expansions of (t) for |t| → 0. | E.M.E.Zayed, I.H.Abdel-Halim Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt E-mail: emezayed@hotmail.com & ismhalim@hotmail.com | 2001 | Acta Mathematica Scientia2001，21，2： | 2 |
| 4 | The Asymptotics of the Two-Dimensional Wave Equation for a General Multi-Connected Vibrating Membrane with Piecewise Smooth Robin Boundary Conditions显示文摘The asymptotic expansion for small |t| of the trace of the wave kernel ∧↑μ(t) =∑v=1^∞exp(-it μv^1/2), where i= √-1 and {μv}v=1^∞ are the eigenvalues of the negative Laplacian -△=-∑β=1^2(δ/δx^β)^2 in the (x^1, x^2)-plane, is studied for a multi-connected vibrating membrane Ω in R^2 surrounded by simply connected bounded domains Ωj with smooth boundaries δΩj(j=1,...,n), where a finite number of piecewise smooth Robin boundary conditions on the piecewise smooth components Гi(i=1+κj-1,...,κj) of the boundaries δΩj are considered, such that δΩj=∪i=1+κj-1^κj Гi and κ0=0. The basic problem is to extract information on the geometry of Ω using the wave equation approach. Some geometric quantities of Ω (e.g. the area of Ω, the total lengths of its boundary, the curvature of its boundary, the number of the holes of Ω, etc.) are determined from the asymptotic expansion of the trace of the wave kernel ∧↑μ(t) for small |t|. | E.M.E.ZAYED | 2004 | Acta Mathematica Sinica,English Series2004，20，2： | 2 |
| 5 | INVERSE PROBLEMS FOR A GENERAL MULTI-CONNECTED BOUNDED DRUM WITH APPLICATIONS IN PHYSICS显示文摘This paper studies the influence of a finite container on an ideal gas. Thetrace of the heat kernelΘ (t) = ∑∞μ=1 exp(-tλμ), where {λμ}μ=1 are the eigenvalues of thenegative Laplacian -△n = - ∑np (a/axp)2 in Rn(n = 2 or 3), is studied for a general multi-connected bounded drum Ω which is surrounded by simply connected bounded domainsof Ω are determined. The thermodynamic quantities for an ideal gas enclosed in Ω areexamined by using the asymptotic expansions of Θ(t) for short-time t. It is shown that theideal gas can not feel the shape of its container Ω, although it can feel some geometricalproperties of it. | E.M.E.Zayed | 2003 | Acta Mathematica Scientia2003，23，1： | 1 |
| 6 | DNA Dynamics Studied Using the Homogeneous Balance Method显示文摘We employ the homogeneous balance method to construct the traveling waves of the nonlinear vibrational dynamics modeling of DNA.Some new explicit forms of traveling waves are given.It is shown that this method provides us with a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.Strengths and weaknesses of the proposed method are discussed. | E.M.E.Zayed A.H.Arnous | 2012 | Chinese Physics Letters2012，29，8： | 1 |
| 7 | Exact Solutions of Kolmogorov-Petrovskii-Piskunov Equation Using the Modified Simple Equation Method显示文摘The modified simple equation method is employed to find the exact solutions of the nonlinear Kolmogorov-Petrovskii-Piskunov(KPP) equation.When certain parameters of the equations are chosen to be special values,the solitary wave solutions are derived from the exact solutions.It is shown that the modified simple equation method provides an effective and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. | E.M.E.Zayed S.A.Hoda Ibrahim | 2014 | Acta Mathematicae Applicatae Sinica2014，30，3： | 1 |
| 8 | Asymptotic Expansions of the Heat Kernel of the Laplacian for General Annular Bounded Domains with Robin Boundary Conditions:Further Results显示文摘The asymptotic expansions of the trace of the heat kernel θ(t)=∑^∞v=1^exp(-tλv) for small positive t,where {λv} are the eigenvalues of the negative Laplacian -△n=-∑^ni=1(D/Dx^1)^2 in R^2(n=2 or 3),are studied for a general annular bounded domain Ω with a smooth inner boundary DΩ1 and a smooth outer boundary DΩ2,where a finite number of piecewise smooth Robin boundary conditions(D/Dnj+γh)Ф=0 on the components Гj(j= 1,...,m) of (DΩ1 and on the components Гj (j=k+1,…,m) of of DΩ2 are considered such that DΩl=U^kj=lГj and DΩ2= U^m=k+1Гj and where the coefficients γj(j=1,...,m) are piecewise smooth positive functions. Some applications of θ(t) for an ideal gas enclosed in the general annular bounded domain Ω are given. Further results are also obtained. | E.M.E.ZAYED | 2003 | Acta Mathematica Sinica,English Series2003，19，4： | 0 |
| 9 | SOME OSCILLATION CRITERIA FOR SECOND ORDER NONLINEAR FUNCTIONAL ORDINARY DIFFERENTIAL EQUATIONS显示文摘这篇文章的主要目的是学习下列非线性的功能的微分方程的答案的摆动的行为 | E.M.E.Zayed M.A.El-Moneam | 2007 | Acta Mathematica Scientia2007，27，3： | 0 |
| 10 | Eigenvalues of the Negative Laplacian for Simply Connected Bounded Domains | E.M.E.Zayed (Mathematics Department,Faculty of Science,Zagazig University,Zagazig,Egypt) | 1997 | Acta Mathematica Sinica,English Series1997，13，3： | 0 |
| 11 | Short-time Asymptotics of the Heat Kernel on Bounded Domain with Piecewise Smooth Boundary Conditions and Its Applications to an Ideal Gas显示文摘The asymptotic expansion of the heat kernel Θ(t) =∑^∞k=1 exp(-tλj) where {λj }^∞j=1 are the eigenvalues of the negative Laplacian -Δn =-∑^nk=1(θ/θx^k)^2 is studied for a general bounded domain Ω with a smooth boundary δΩ. In this paper, we consider the case of a finite number of the Dirichlet conditions Φ= 0 on Γi (i = 1, ..., J) and the Neumann conditions δΦ/δvi = 0 on Γi (i = J+1,..., k) and the Robin conditions (δ/δvi +γi)Φ=0 on Γi (i=k+1,..., m) where γi are piecewise smooth positive impedance functions, such that δΩ consists of a finite number of piecewise smooth components Γi (i=1,..., m) where δΩ =∪^m i=1 Γi. We construct the required asymptotics in the form of a power series over t. The senior coefficients in this series are specified as functionals of the geometric shape of the domain Ω. This result is applied to calculate the one-particle partition function of a 'special ideal gas', i.e., the set of non-interacting particles set up in a box with Dirichlet, Neumann and Robin boundary conditions for the appropriate wave function. Calculation of the thermodynamic quantities for the ideal gas such as the internal energy, pressure and specific heat reveals that these quantities alone are incapable of distinguishing between two different shapes of the domain. This conclusion seems to be intuitively clear because it is based on a limited information given by a one-particle partition function; nevertheless, its formal theoretical motivation is of some interest. | E.M.E.ZAYED | 2004 | Acta Mathematicae Applicatae Sinica2004，20，2： | 0 |
| 12 | The 3D Inverse Problem of the Wave Equation for a General Multi-connected Vibrating Membrane with a Finite Number of Piecewise Smooth Boundary Conditions显示文摘在帽子(t) exp 上的波浪核(亩)的踪迹(在哪儿的-itE(omega)(1/2)){电子终止}( omega=1 )(无穷)是否定拉普拉斯算符-del(2)= -Sigma(k=1)(3)in 的特征值( x ( 1 ), x ( 2 ), x ( 3 ))空格为许多围住的域被学习,在此无穷< | E.M.E.ZAYED | 2005 | Acta Mathematica Sinica,English Series2005，21，4： | 0 |
| 13 | Generalized and Improved(G′/G)-Expansion Method Combined with Jacobi Elliptic Equation显示文摘In this article, we propose an alternative approach of the generalized and improved(G′/G)-expansion method and build some new exact traveling wave solutions of three nonlinear evolution equations, namely the Boiti–Leon–Pempinelle equation, the Pochhammer–Chree equations and the Painleve integrable Burgers equation with free parameters. When the free parameters receive particular values, solitary wave solutions are constructed from the traveling waves. We use the Jacobi elliptic equation as an auxiliary equation in place of the second order linear equation. It is established that the proposed algorithm offers a further influential mathematical tool for constructing exact solutions of nonlinear evolution equations. | M.Ali Akbar Norhashidah Hj.Mohd.Ali E.M.E.Zayed | 2014 | Communications in Theoretical Physics2014，61，6： | 0 |
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