Exact solution of the discrete Schrödinger equation for ferromagnetic chains

It is shown that Bethe's exact solution for the finite Heisenberg ferromagnetic chain can be obtained via a direct Fourier transform. Unlike the Bethe ansatz approach, the latter is not confined to one space dimension and opens the possibility of obtaining exact solutions in higher dimensions.     

Scattering in a Pekeris waveguide from a rough bottom using a two-way coupled mode approach

Scattering from a rough ocean bottom is described numerically with a two-way coupled-mode formalism that contains scattering effects to all orders and provides an exact solution to the wave equation. Both scattered field and direct blast components are computed within the formalism framework. A comparison of the scattered component solution from the coupled mode with the Born approximation (BA) solution for scattering from a rough bottom Pekeris waveguide shows that the BA predicts correctly the scattered field levels but not detailed structure. The transition from direct blast to scattered field dominance is identified in the total field time series.     

A certain critical two-soliton solution of the nonlinear Schroedinger equation

An exact two-soliton solution of the nonlinear Schroedinger equation is derived by using the Hirota direct approach. This solution describes such a critical process that two still solitons separated infinitely approach and then pass through each other and keep straight on infinitely.     

A DIRECT PERTURBATION THEORY OF THE NONLINEAR SCHR?DINGER EQUATION WITH CORRECTIONS

An exact direct perturbation theory of nonlinear Schrodinger equation with corrections is developed under the condition that the initial value of the perturbed solution is equal to the value of an exact multisoliton solution at a particular time. After showing the squared Jost functions are the eigenfunctions of the linearized operator with a vanishing eigenvalue,suitable definitions of adjoint functions and inner product are introduced. Orthogonal relations are derived and the expansion of the unity in terms of the squared Jost functions is naturally implied. The completeness of the squared Jost functions is shown by the generalized Marchenko equation. As an example,the evolution of a Raman loss compensated soliton in an optical fiber is treated.     

A new similarity solution of the Burgers equation with linear damping

The direct method of Clarkson and Kruskal is used to study the symmetry reductions of the Burgers equation with linear damping. The classical similarity reductions reported previously is recovered. The new, nonclassical similarity reduction is obtained. The new similarity solution is given, and it is also obtained by means of the singular manifold method. The nonclassical method is used to demonstrate that the new exact solution is indeed a nonclassical similarity solution. This work has been supported by the Postdoctoral Science Foundation of China.     

VIBRATIONS OF NON-UNIFORM CONTINUOUS BEAMS UNDER MOVING LOADS

The dynamic behavior of multi-span non-uniform beams transversed by a moving load at a constant and variable velocity is investigated. The continuous beam is modelled using Bernoulli-Euler beam theory. The solution is obtained by using both the modal analysis method and the direct integration method. The natural frequencies and mode shapes used in the solution of this problem are obtained exactly by deriving the exact dynamic stiffness matrices for any polynomial variation of the cross-section along the beam using the exact element method. The mode shapes are expressed as infinite polynomial series. Using the exact mode shapes yields the exact solution for general variation of the beam section in case of constant and variable velocity. Numerical examples are presented in order to demonstrate the accuracy and the effectiveness of the present study, and the results are compared to previously published results.     

皮秒类提升脉冲串的产生与传输

通过函数和变量变换给出变系数非线性薛定谔方程的一个新的精确解,它可以用来描述非均匀光纤中的调制不稳定过程.基于这个精确解我们给出一类新的类提升脉冲串,并讨论该脉冲串的传输特性.结果表明,当类提升脉冲串能量大于某一阈值时类提升脉冲串可以稳定传输.同时我们还比较指数控制系统和理想系统中类提升脉冲串的传输,结果表明选择合适的控制系统可以抑制脉冲间的相互作用,这对增加光通信的传输比特率是非常有益的.     

Dynamics of NLS solitons described by the cubic-quintic Ginzburg-Landau equation

The generalized moment method is applied to average the Ginzburg-Landau equation with quintic nonlinearity in the neighborhood of a soliton solution to the nonlinear Schrödinger equation. A qualitative analysis of the resulting dynamical system is presented. New soliton solutions bifurcating from a known exact soliton solution are obtained. The results of the qualitative analysis are compared with those obtained by direct numerical solution of the Ginzburg-Landau equation.     

Exact Soliton Solution of Nonlinear Evolution in Ice-Like Structures

The exact soliton solution with a good convergency for nonlinear problem which describes proton motion in a system with ice-like structure is obtained by using a renormalized condition of the expansion coefficients in addition to a direct algebraic method.     

Exact solution of Maxwell's equations for optical interactions with a macroscopic random medium

We report what we believe to be the first rigorous numerical solution of the two-dimensional Maxwell equations for optical propagation within, and scattering by, a random medium of macroscopic dimensions. Our solution is based on the pseudospectral time-domain technique, which provides essentially exact results for electromagnetic field spatial modes sampled at the Nyquist rate or better. The results point toward the emerging feasibility of direct, exact Maxwell equations modeling of light propagation through many millimeters of biological tissues. More generally, our results have a wider implication: Namely, the study of electromagnetic wave propagation within random media is moving toward exact rather than approximate solutions of Maxwell's equations.     

Inverse Problem of the Theory of Reflection for Three-Layer Structures

Journal of Experimental and Theoretical Physics - We propose an original approach to analyzing the exact solution of the direct problem in the theory of reflection that allows an algorithm for...     

Direct discontinuous Galerkin method for the generalized Burgers—Fisher equation

In this study, we use the direct discontinuous Galerkin method to solve the generalized Burgers-Fisher equation. The method is based on the direct weak formulation of the Burgers-Fisher equation. The two adjacent cells are jointed by a numerical flux that includes the convection numerical flux and the diffusion numerical flux. We solve the ordinary differential equations arising in the direct Galerkin method by using the strong stability preserving Runge-Kutta method. Numerical results are compared with the exact solution and the other results to show the accuracy and reliability of the method.     

Direct transference applied to the study of room acoustics

In a recent article Kruzins and Fricke [1] applied the method of Markov chains to represent the “random walk” of phonons inside an enclosed space and to predict stationary state acoustic pressure levels, at sufficiently high frequencies, in geometrically complex spaces. In this paper it is demonstrated that with the same initial hypothesis the exact solution can be obtained directly by using the method of direct transference. Explicit expressions for the coefficients of the solution matrix are found, their physical significance is made evident, and a simple method for calculating the solution is presented.     

Index to volume 72

A numerical analysis of wave propagation in one dimensional inhomogeneous media is presented in this paper, the first (Part I) of two companion papers. The aim is to provide a natural and physical basis for the solution of the inverse scattering problem in one dimension. The paper includes (i) a discussion of some aspects of the numerical solution of the direct problem, (ii) typical results of calculation and (iii) a comparison between exact solutions and forward scattering approximation (FSA) solutions of the direct problem. It is shown that the FSA allows accurate calculations of the reflected wave and thus constitutes a sound basis for the solution of the inverse problem treated in Part II.     

Elastic analysis of an elliptic notch in quasicrystals of point group 10 subjected to shear loading

Based on the stress potential and complex variable function method, this paper makes an elastic analysis of an elliptic notch subjected to uniform shear stress at infinity in quasicrystals with point group 10. With the aid of conformal transformation, an exact solution for the elliptic notch of the quasicrystals is obtained. The solution of the mode {\rm II} Griffith crack as a special case is constructed. The stress intensity factor and energy release rate have been also obtained as a direct result of the crack solution.     

A New Multisoliton Solution to (2+1)-Dimensional KdV Equation

A new multisoliton solution to the (2+1)-dimensional KdV equation is obtained by means of the truncated Painleve expansion method and a direct ansatz technique. This new exact solution is periodic in the propagating direction x and exponentially decaying in y and thus it is called periodic solitons. A typical spatial structure of it is illustrated by the figures.     

Solution of the inverse radiative load problem in a two-dimensional system

An inverse radiation analysis is presented for estimating the temperature and the heat load distributions of the heating surface from the temperature and the heat flux measurements of the heated object. The Monte Carlo method is employed to solve the direct radiation problem. The inverse radiation problem is solved using the conjugate gradient and singular value decomposition methods. The measured data are simulated by adding random errors to the exact solution of the direct problem. The effects of the measurement errors on the accuracy of the inverse analysis are investigated. The study shows that the heat load distribution of the heating surface can be estimated accurately for the exact and noisy data. And the conjugate gradient method is better than the singular value decomposition method since the former can obtain more accurate results if the measurement errors are the same.     

Finite Symmetry Transformation Groups and Exact Solutions of Konopelchenko-Dubrovsky Equation

Based on the general direct method developed by Lou et al. [J. Phys. A: Math. Gen. 38 (2005) L129], the symmetry group theorem is obtained,from that both the Lie point groups and the non-Lie symmetry groups of the Konopelchenko-Dubrovsky (KD) equation are obtained. From the theorem, some exact solutions of KD equation are derived from a simple travelling wave solution and a multi-soliton solution.     

N-Soliton Solution in Wronskian Form for a Generalized Variable-Coefficient Korteweg--de Vries Equation

We concentrate on finding exact solutions for a generalized variable-coefficient Korteweg-de Vries equation of physically significance. The analytic N-soliton solution in Wronskian form for such a model is postulated and verified by direct substituting the solution into the bilinear form by virtue of the Wronskian technique. Additionally, the bilinear auto-Backlund transformation between the （ N - 1）- and N-soliton solutions is verified.