Green's functions of the forced vibration of Timoshenko beams with damping effect

This paper is concerned with the dynamic solutions for forced vibrations of Timoshenko beams in a systematical manner. Damping effects on the vibrations of the beam are taken into consideration by introducing two characteristic parameters. Laplace transform method is applied in the present study and corresponding Green's functions are presented explicitly for beams with various boundaries. The present solutions can be readily reduced to those for others classical beam models by setting corresponding parameters to zero or infinite. Numerical calculations are performed to validate the present solutions and the effects of various important physical parameters are investigated.     

MODES OF CONTACT AND UNIQUENESS OF SOLUTIONS FOR SYSTEMS WITH FRICTION-AFFECTED SLIDERS

The kinetic equations of planar multi-body systems with friction-affected sliding joints are reformulated for the computation of closed-form solutions for the kinetic parameters. The state of such systems is characterized not only by the position parameters and velocities, but in addition, the modes of contact in the sliding joints must be specified. Then the cases with one or several sets of solutions, obtained for the same position parameters, velocities, active forces and friction parameters, can be related to positions of the system with different modes of contact between sliders and guiding surfaces. They are physical unequivocal states and can be interpreted as unique solutions for the kinetic problem with specified configuration of the system. If no solutions exist, then the friction parameters considered are too large and exceed limiting values, for which friction locking occurs.     

Finding Solutions to Equations for the Longitudinal Components of an Electromagnetic Field in a Biisotropic Medium in the Neighborhood of a Regular Singular Point as Generalized Power Series

For a system of equations that describe electromagnetic fields in a biisotropic medium, particular solutions have been constructed in the neighborhood of a regular singular point. The solutions are written in the form of generalized power series. For the coefficients of the power series, exponents and recursion relations have been found. It has been shown that the solutions of the wave equations are generalizations of well-known special cylindrical functions. The behavior of the particular solutions have been examined for varied material parameters of the medium. The solutions obtained allow one to formulate mathematical models which could be used to calculate and optimize the parameters of a wide spectrum of functional devices based on waveguide structures with biisotropic inserts.     

Quasi-periodic solutions and asymptotic properties for the nonlocal Boussinesq equation

We construct the Hirota bilinear form of the nonlocal Boussinesq(nlBq) equation with four arbitrary constants for the first time. It is special because one arbitrary constant appears with a bilinear operator together in a product form. A straightforward method is presented to construct quasiperiodic wave solutions of the nl Bq equation in terms of Riemann theta functions. Due to the specific dispersion relation of the nl Bq equation, relations among the characteristic parameters are nonlinear, then the linear method does not work for them. We adopt the perturbation method to solve the nonlinear relations among parameters in the form of series. In fact, the coefficients of the governing equations are also in series form.The quasiperiodic wave solutions and soliton solutions are given. The relations between the periodic wave solutions and the soliton solutions have also been established and the asymptotic behaviors of the quasiperiodic waves are analyzed by a limiting procedure.     

Soliton solutions in some non-linear Schrödinger-like equations

Soliton solutions are obtained for a class of non-linear Schrödinger-like equations. The parameters of the soliton solutions are written out explicitly.     

Exact solutions of a Fokker-Planck equation

Exact explicit solutions are given for a one-dimensional Fokker-Planck equation with a particular potential form involving hyperbolic functions. This potential contains four arbitrary parameters that can be chosen so that the potential is bistable. The solutions also contain parameters that can be chosen so that the initial distribution is approximately Gaussian, centered either at the unstable potential maximum or in the neighborhood of the secondary minimum. The use of the solutions to approximate solutions for other potentials is considered.     

A study of the discrete Pv equation: Miura transformations and particular solutions

We derive the form of the Miura transformation of the discrete P_v equation and show that it is indeed an auto-Bäcklund transformation, i.e. it relates the discrete P_v to itself. Using this auto-Bäcklund, we obtain the Schlesinger transformations of discrete P_v which relate the solution for one set of the parameters of the equation to that of another set of neighbouring parameters. Finally, we obtain particular solutions of the discrete P_v (i.e. solutions that exist only for some specific values of the parameters). These solutions are of two types: solutions involving the confluent hypergeometric function (on codimension-one submanifold of parameters) and rational solutions (on codimension-two submanifold of parameters).     

The (<Emphasis Type="Italic">G′/G</Emphasis>)-expansion method for a discrete nonlinear Schrödinger equation

An improved algorithm is devised for using the (G′/G)-expansion method to solve nonlinear differential-difference equations. With the aid of symbolic computation, we choose a discrete nonlinear Schrödinger equation to illustrate the validity and advantages of the improved algorithm. As a result, hyperbolic function solutions, trigonometric function solutions and rational solutions with parameters are obtained, from which some special solutions including the known solitary wave solution are derived by setting the parameters as appropriate values. It is shown that the improved algorithm is effective and can be used for many other nonlinear differential-difference equations in mathematical physics.     

Modulation instability analysis,optical and other solutions to the modified nonlinear Schrödinger equation

This paper studies the new families of exact traveling wave solutions with the modified nonlinear Schrödinger equation, which models the propagation of rogue waves in ocean engineering. The extended Fan sub-equation method with five parameters is used to find exact traveling wave solutions. It has been observed that the equation exhibits a collection of traveling wave solutions for limiting values of parameters. This method is beneficial for solving nonlinear partial differential equations, because it is not only useful for finding the new exact traveling wave solutions, but also gives us the solutions obtained previously by the usage of other techniques (Riccati equation, or first-kind elliptic equation, or the generalized Riccati equation as mapping equation, or auxiliary ordinary differential equation method) in a combined approach. Moreover, by means of the concept of linear stability, we prove that the governing model is stable. 3D figures are plotted for showing the physical behavior of the obtained solutions for the different values of unknown parameters with constraint conditions.     

Determination of Wolfenstein Parameters in NN Scattering Directly from Observables

The Wolfenstein parameters are for the first time obtained analytically in terms of observables. It is shown that a set of ten nucleon?Cnucleon (NN) observables, which contains polarization observables together with the differential cross section, determines uniquely the solution for Wolfenstein parameters except for a common insignificant phase. Using such analytical solutions one expects to get more accurate theoretical parameters for the potential models by ?? ² fitting to the resulting Wolfenstein parameter data than the standard manner of a phase-shift analysis. An example of fixing a unique set of physical solutions for the Wolfenstein parameters from a set of 16 solutions based on nine observables alone and adding one more observable is illustrated using pseudo data generated by the CD Bonn potential.     

Nonlinear dispersion of a pollutant ejected into a channel flow

In this paper, we study the nonlinear coupled boundary value problem arising from the nonlinear dispersion of a pollutant ejected by an external source into a channel flow. We obtain exact solutions for the steady flow for some special cases and an implicit exact solution for the unsteady flow. Additionally, we obtain analytical solutions for the transient flow. From the obtained solutions, we are able to deduce the qualitative influence of the model parameters on the solutions. Furthermore, we are able to give both exact and analytical expressions for the skin friction and wall mass transfer rate as functions of the model parameters. The model considered can be useful for understanding the polluting situations of an improper discharge incident and evaluating the effects of decontaminating measures for the water bodies.     

The extended Fan's sub-equation method and its application to KdV–MKdV,BKK and variant Boussinesq equations

An extended Fan's sub-equation method is used for constructing exact travelling wave solutions of nonlinear partial differential equations (NLPDEs). The key idea of this method is to take full advantage of the general elliptic equation involving five parameters which has more new solutions and whose degeneracies can lead to special sub-equations involving three parameters. More new solutions are obtained for KdV–MKdV, Broer–Kaup–Kupershmidt (BKK) and variant Boussinesq equations. Then we present a technique which not only gives us a clear relation among this general elliptic equation and other sub-equations involving three parameters (Riccati equation, first kind elliptic equation, auxiliary ordinary equation, generalized Riccati equation and so on), but also provides an approach to construct new exact solutions to NLPDEs.     

A Pair of Resonance Stripe Solitons and Lump Solutions to a Reduced(3+1)-Dimensional Nonlinear Evolution Equation

With symbolic computation, some lump solutions are presented to a(3+1)-dimensional nonlinear evolution equation by searching the positive quadratic function from the Hirota bilinear form of equation. The quadratic function contains six free parameters, four of which satisfy two determinant conditions guaranteeing analyticity and rational localization of the solutions, while the others are free. Then, by combining positive quadratic function with exponential function, the interaction solutions between lump solutions and the stripe solitons are presented on the basis of some conditions. Furthermore, we extend this method to obtain more general solutions by combining of positive quadratic function and hyperbolic cosine function. Thus the interaction solutions between lump solutions and a pair of resonance stripe solitons are derived and asymptotic property of the interaction solutions are analyzed under some specific conditions. Finally, the dynamic properties of these solutions are shown in figures by choosing the values of the parameters.     

Static,Spherically Symmetric Solutions of Yang-Mills-Dilaton Theory

Static, spherically symmetric solutions of the Yang-Mills-Dilaton theory are studied. It is shown that these solutions fall into three different classes. The generic solutions are singular. Besides there is a discrete set of globally regular solutions further distinguished by the number of nodes of their Yang-Mills potential. The third class consists of oscillating solutions playing the role of limits of regular solutions, when the number of nodes tends to infinity. We show that all three sets of solutions are non-empty. Furthermore we give asymptotic formulae for the parameters of regular solutions and confront them with numerical results.     

Analytical and numerical solutions of the density dependent diffusion Nagumo equation

In this Letter, we obtained solutions to a class of density dependent diffusion Nagumo equations. In particular, series solutions are obtained, along with a bound for the range of the convergence. Also, numerical solutions are obtained by the Runge-Kutta-Fehlberg 45 method. Moreover, the dependence of the traveling wave solutions on various parameters is discussed. Furthermore, we compare the series solutions with the numerical solutions to validate the numerical method. The results obtained in this study reveal many interesting behaviors that warrant further study on the Nagumo equation.     

Deriving the New Traveling Wave Solutions for the Nonlinear Dispersive Equation,KdV-ZK Equation and Complex Coupled KdV System Using Extended Simplest Equation Method

In this paper, we investigate the traveling wave solutions for the nonlinear dispersive equation, Korteweg-de Vries Zakharov-Kuznetsov (KdV-ZK) equation and complex coupled KdV system by using extended simplest equation method, and then derive the hyperbolic function solutions include soliton solutions, trigonometric function solutions include periodic solutions with special values for double parameters and rational solutions. The properties of such solutions are shown by figures. The results show that this method is an effective and a powerful tool for handling the solutions of nonlinear partial differential equations (NLEEs) in mathematical physics.     

Matching in a class of stationary axisymmetric perfect fluid solutions of Einstein's equations

The class of previously found stationary axisymmetric perfect fluid solutions of Einstein's equations is written inh-orthogonal coordinates,h being a space-like coordinate. Matching of a big number of solutions of the class with each other seems to be possible for a proper choice of some parameters. The exterior solutions of the class are matched explicitly with interior solutions. Also, interior solutions are matched explicitly with each other.     

General nonextremal rotating black holes in minimal five-dimensional gauged supergravity

We construct the general solution for nonextremal charged rotating black holes in five-dimensional minimal gauged supergravity. They are characterized by four nontrivial parameters: namely, the mass, the charge, and the two independent rotation parameters. The metrics in general describe regular rotating black holes, providing the parameters lie in appropriate ranges so that naked singularities and closed timelike curves (CTCs) are avoided. We calculate the conserved energy, angular momenta, and charge for the solutions, and show how supersymmetric solutions arise in a Bogomol'nyi-Prasad-Sommerfield limit. These have naked CTCs in general, but for special choices of the parameters we obtain new regular supersymmetric black holes or smooth topological solitons.     

Controllable Discrete Rogue Wave Solutions of the Ablowitz-Ladik Equation in Optics

With the aid of symbolic computation Maple, the discrete Ablowitz-Ladik equation is studied via an algebra method, some new rational solutions with four arbitrary parameters are constructed. By analyzing related parameters, the discrete rogue wave solutions with alterable positions and amplitude for the focusing Ablowitz-Ladik equations are derived. Some properties are discussed by graphical analysis, which might be helpful for understanding physical phenomena in optics.     

Quantization of superparametrized monopoles

Classical finite-energy solutions of the SU(2) Yang-Mills-Higgs system in four-dimensional space-time are embedded in the supersymmetric extension of the theory. Finite supertranslations are constructed and are used to obtain a family of solutions to the supersymmetric field equations, parametrized by fermionic Majorana spinor parameters. The quantum theory around arbitrary classical solutions, parametrized by arbitrary bosonic (global and local) as well as fermionic (global) parameters, is constructed and discussed.