基于行波分解的泛频响函数法在高承台桩灾后无损检测评估中的应用研究

针对现有方法在高承台桩灾后无损检测和评估中的局限性,提出了基于行波分解的泛频响函数法。将承台对桩顶的作用简化为黏弹性支撑边界,采用自行编制的波动分析程序求得检测截面处的泛频响函数;通过在该位置虚拟输入半正弦激励脉冲,将泛频响函数所包含的信息转换到时域内进行分析,得到检测截面以下虚拟隔离单桩桩顶的速度时域响应曲线;分析了相关参数对泛频响函数和由此转换而来的时域响应的影响。结果表明,基于行波分解的泛频响函数法,能在不破坏上部结构的前提下,完全消除其对检测结果的影响,从而将复杂结构体系下的基桩转化到单桩模式下进行检测分析,简化了检测步骤,降低了分析难度。

基于经验小波变换的电力线路多级状态检测

为提高电力线路状态检测的精准度,最大程度上避免故障误检、漏检,使检测工作向信息化与自动化方向发展,提出基于经验小波变换的电力线路多级状态检测方法。仿真结果表明,所提方法可以有效检测电力线路故障状态,且定位精准度高,能够有效提高检测设备的稳定性,可作为保障电力系统正常运行的重要屏障。

A General Mapping Approach and New Travelling Wave Solutions to（2＋1）-Dimensional Boussinesq Equation

A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.

All Single Traveling Wave Solutions to （3＋1）-Dimensional Nizhnok-Novikov-Veselov Equation

Using elementary integral method, a complete classification of all possible exact traveling wave solutions to （3＋1）-dimensional Nizhnok-Novikov-Veselov equation is given. Some solutions are new.

Exact Solutions of the Harry-Dym Equation

The aim of this paper is to generate exact travelling wave solutions of the Harry-Dym equation through the methods of Adomian decomposition, He＇s variational iteration, direct integration, and power series. We show that the two later methods are more successful than the two former to obtain more solutions of the equation.

Bifurcations of Exact Traveling Wave Solutions for(2+1)-Dimensional HNLS Equation

For the(2+1)-Dimensional HNLS equation,what are the dynamical behavior of its traveling wave solutions and how do they depend on the parameters of the systems? This paper will answer these questions by using the methods of dynamical systems.Ten exact explicit parametric representations of the traveling wave solutions are given.

A Computational Approach to the New Type Solutions of Whitham-Broer-KaupEquation in Shallow Water

Based on computerized symbolic computation,a new method and its algorithm are proposed for searching for exact travelling wave solutions of the nonlinear partial differential equations.Making use of our approach,we investigate the Whitham-Broer-Kaup equation in shallow water and obtain new families of exact solutions,which include soliton-like solutions and periodic solutions.As its special cases,the solutions of classical long wave equations and modified Boussinesq equations can also be found.

Using Symbolic Computation to Exactly Solve the Integrable Broer-Kaup Equations in （2＋1）-Dimensional Spaces

The extended tanh method is further improved by generalizing the Riccati equation and introducing its twenty seven new solutions. As its application, the (2+ 1)-dimensional Broer-Kaup equation is investigated and then its fifty four non-travelling wave solutions have been obtained. The results reported in this paper show that this method is more powerful than those, such as tanh method, extended tanh method, modified extended tanh method and Riccati equation expansion method introduced in previous literatures.

Application of Modified G'/G-Expansion Method to Traveling Wave Solutions for Whitham-Broer-Kaup-Like Equations

A modified G′/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham -Broer- Kaup-Like equations. As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained. When the parameters are taken as special values the solitary wave solutions can be obtained.

Travelling Wave Solutions to Stretched Beam's Equation: Phase Portraits Survey

In this paper, following the phase portraits analysis, we investigate the integrability of a system which physically describes the transverse oscillation of an elastic beam under end-thrust. As a result, we find that this system actually comprises two families of travelling waves： the sub- and super-sonic periodic waves of positive- and negative- definite velocities, respectively, and the localized sub-sonic loop-shaped waves of positive-definite velocity. Expressing the energy-like of this system while depicting its phase portrait dynamics, we show that these multivaiued localized travelling waves appear as the boundary solutions to which the periodic travelling waves tend asymptotically

Applications of Extended Mapping Deformation Method in Two （3＋1）-Dimensional Nonlinear Models

Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.

New Explicit and Exact Travelling Wave Solutions for Burgers-Kolmogorov-Petrovskii-Piscounov Equations

In this paper, many new explicit and exact travelling wave solutions for Burgers-Kolmogorov-Petrovskii-Piscounov(Burgers-KPP) equations are obtained by using hyperbola function method and Wu-elimination method, which include new singular solitary wave solutions and periodic solutions. Particular important cases of the equation, such as the generalized Burgers-Fisher equation, Burgers-Chaffee infante equation and KPP equation, the corresponding solutions can be obtained also. The method can also solve other nonlinear partial differential equations.

Direct Reduction and Exact Solutions for Generalized Variable Coefficients 2D KdV Equation under Some Integrability Conditions

Based on the closed connections among the homogeneous balance （HB） method and Clarkson-KruSkal （CK） method, we study the similarity reductions of the generalized variable coefficients 2D KdV equation. In the meantime it is shown that this leads to a direct reduction in the form of ordinary differential equation under some integrability conditions between the variable coefficients. Two different cases have been discussed, the search for solutions of those ordinary differential equations yielded many exact travelling and solitonic wave solutions in the form of hyperbolic and trigonometric functions under some constraints between the variable coefficients.

T-transformation Method for Studing the Multi-solitone Solutions of the Korteveg-de Vries Type Equations

In this paper, we propose a new technique of finding the PDE＇s traveling wave solutions based on the T-transformations. Using T-representation method we find a new class ofKorteveg-de Vries solution and propose method for studing the multi-solitone solutions of the Korteveg-de Vries type equations.

Travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation

The travelling wave solutions of a generalized Camassa-Holm-Degasperis-Procesi equation ut-uxxt + (1 + b)umux = buxuxx + uuxxx are considered where b > 1 and m are positive integers. The qualitative analysis methods of planar autonomous systems yield its phase portraits. Its soliton wave solutions, kink or antikink wave solutions, peakon wave solutions, compacton wave solutions, periodic wave solutions and periodic cusp wave solutions are obtained. Some numerical simulations of these solutions are also given.

High efficient parallel numerical surface wave model based on an irregular quasi-rectangular domain decomposition scheme

To achieve high parallel efficiency for the global MASNUM surface wave model, the algorithm of an irregular quasirectangular domain decomposition and related serializing of calculating points and data exchanging schemes are developed and conducted, based on the environment of Message Passing Interface(MPI). The new parallel version of the surface wave model is tested for parallel computing on the platform of the Sunway BlueLight supercomputer in the National Supercomputing Center in Jinan. The testing involves four horizontal resolutions, which are 1°×1°,(1/2)°×(1/2)°,(1/4)°×(1/4)°, and(1/8)°×(1/8)°. These tests are performed without data Input/Output(IO) and the maximum amount of processors used in these tests reaches to 131072. The testing results show that the computing speeds of the model with different resolutions are all increased with the increasing of numbers of processors. When the number of processors is four times that of the base processor number, the parallel efficiencies of all resolutions are greater than 80%. When the number of processors is eight times that of the base processor number, the parallel efficiency of tests with resolutions of 1°×1°,(1/2)°×(1/2)° and(1/4)°×(1/4)° is greater than 80%, and it is 62% for the test with a resolution of(1/8)°×(1/8)° using 131072 processors, which is the nearly all processors of Sunway BlueLight. When the processor's number is 24 times that of the base processor number, the parallel efficiencies for tests with resolutions of 1°×1°,(1/2)°×(1/2)°, and(1/4)°×(1/4)° are 72%, 62%, and 38%, respectively. The speedup and parallel efficiency indicate that the irregular quasi-rectangular domain decomposition and serialization schemes lead to high parallel efficiency and good scalability for a global numerical wave model.

Traveling Wave Solutions for Nonlinear Differential-Difference Equations of Rational Types

Differential-difference equations are considered to be hybrid systems because the spatial variable n is discrete while the time t is usually kept continuous.Although a considerable amount of research has been carried out in the field of nonlinear differential-difference equations,the majority of the results deal with polynomial types.Limited research has been reported regarding such equations of rational type.In this paper we present an adaptation of the(G /G)-expansion method to solve nonlinear rational differential-difference equations.The procedure is demonstrated using two distinct equations.Our approach allows one to construct three types of exact traveling wave solutions(hyperbolic,trigonometric,and rational) by means of the simplified form of the auxiliary equation method with reduced parameters.Our analysis leads to analytic solutions in terms of topological solitons and singular periodic functions as well.

Shape Analysis of Bounded Traveling Wave Solutions and Solution to the Generalized Whitham-Broer-Kaup Equation with Dissipation Terms

This paper deals with the problem of the bounded traveling wave solutions' shape and the solution to the generalized Whitham-Broer-Kaup equation with the dissipation terms which can be called WBK equation for short.The authors employ the theory and method of planar dynamical systems to make comprehensive qualitative analyses to the above equation satisfied by the horizontal velocity component u(ξ) in the traveling wave solution (u(ξ),H(ξ)),and then give its global phase portraits.The authors obtain the existent conditions and the number of the solutions by using the relations between the components u(ξ) and H(ξ) in the solutions.The authors study the dissipation effect on the solutions,find out a critical value r*,and prove that the traveling wave solution (u(ξ),H(ξ)) appears as a kink profile solitary wave if the dissipation effect is greater,i.e.,|r| ≥ r*,while it appears as a damped oscillatory wave if the dissipation effect is smaller,i.e.,|r| < r*.Two solitary wave solutions to the WBK equation without dissipation effect is also obtained.Based on the above discussion and according to the evolution relations of orbits corresponding to the component u(ξ) in the global phase portraits,the authors obtain all approximate damped oscillatory solutions (u(ξ),H(ξ)) under various conditions by using the undetermined coefficients method.Finally,the error between the approximate damped oscillatory solution and the exact solution is an infinitesimal decreasing exponentially.

Exact Solutions for a Local Fractional DDE Associated with a Nonlinear Transmission Line

Of recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differential-difference equations. This study is devoted to a local fractional differential-difference equation which is related to a nonlinear electrical transmission line. Explicit traveling wave solutions(kink/antikink solitons, singular,periodic, rational) are obtained via the discrete tanh method coupled with the fractional complex transform.

EVANS FUNCTIONS AND ASYMPTOTIC STABILITY OF TRAVELING WAVE SOLUTIONS

This paper studies the asymptotic stability of traveling we solutions of nonlinear systems of integral-differential equations. It has been established that linear stability of traveling waves is equivalent to nonlinear stability and some "nice structure" of the spectrum of an associated operator implies the linear stability. By using the method of variation of parameter, the author defines some complex analytic function, called the Evans function. The zeros of the Evans function corresponds to the eigenvalues of the associated linear operator. By calculating the zeros of the Evans function, the asymptotic stability of the travling wave solutions is established.