new exact solutions of the broer kaup equations in 2 1 dimensional spaces abstract with the aid of maple several new kinds of exact solutions for the broer kaup equations in 2 1 dimensional spaces are obtained by using a new ansatz this approach can also be applied to other nonlinear evolution equations

application of fuzzy control to an inserting operation abstract because of the difficulty of dynamic equations for the inserting operation and the advantage of fuzzy control for easy execution without knowledge of the mathematical models we used the force feedback signal measured by a force sensor and a fuzzy controller to regulate the position of the peg the control strategies include two control loops in one a pid position controller move the peg vague position near to the hole and in the other the fuzzy controller regulates the final position according to contact force between the two control loops we use an index to activate a switch to verify the proposed control strategy we performed experiments with a cartesian manipulator system driven by ac servo motors the experimental results reveal that we can insert a peg into a hole with a fitting clearance less than 0 01 mm

special solutions from the variable separation approach the davey stewartson equation a variable separation procedure for the davey stewartson ds equation is proposed by using a prior ansatz to its bilinear form the reduced equations for two variable separated fields have the same trilinear form although they possess different independent variables the trilinear equation can be changed to a spacetime symmetric form and can be solved by means of a boussinesq type equation system whenever a pair of solutions of the reduced fields are obtained a corresponding solution of the ds equation can be obtained algebraically the single dromion solution and some kinds of positon solutions are obtained explicitly

a review of the decomposition method in applied mathematics abstract the decomposition method can be an effective procedure for analytical solution of a wide class of dynamical systems without linearization or weak nonlinearity assumptions closure approximations perturbation theory or restrictive assumptions on stochasticitiy

on invariant analysis of some time fractional nonlinear systems of partial differential equations i an investigation of lie point symmetries for systems of time fractional partial differential equations including ito system coupled burgers equations coupled korteweg de vries equations hirota satsuma coupled kdv equations and coupled nonlinear hirota equations has been done using the obtained symmetries each one of the systems is reduced to the nonlinear system of fractional ordinary differential equations involving erdelyi kober fractional differential operator depending on a parameter

stochastic exact solutions of the wick type stochastic nls equation based upon the hermite transformation and the extended sub equation expansion method soliton like solutions of the stochastic schrodinger equation in the white noise environment are obtained via maple

using reciprocity to derive the far field displacements due to buried sources and scatterers it is shown that elastodynamic reciprocity provides a simpler approach for deriving the far field displacements due to buried sub surface sources in a half space compared with integral transform techniques the auxiliary fields employed in this approach are the fields associated with the reflection of plane waves of the three possible polarisations and the required far field can be expressed in terms of these well known auxiliary fields the crucial step in this approach is to evaluate a surface integral involving cross work terms between an outgoing spherical wavefront and the auxiliary fields consisting of incident and reflected plane waves this integral can be evaluated by the stationary phase approximation for the two dimensional case or by a generalisation of this approximation for the three dimensional case although this evaluation involves several distinct contributions the final result is shown to be very simple and it can be interpreted as a generalisation of a known result for the one d

fractional burgers equation with nonlinear non locality we consider the viscous burgers equation with a fractional nonlinear term as a model involving non local nonlinearities in conservation laws which surprisingly has an analytical solution obtained by a fractional extension of the hopfcole transformation we use this model and its inviscid limit to develop stable spectral and discontinuous galerkin spectral element methods by employing the concept of spectral vanishing viscosity svv for the global spectral method svv is very effective and the computational cost is o n2 which is essentially the same as for the standard burgers equation we also develop a local discontinuous galerkin ldg spectral element method to improve the accuracy around discontinuities and we again stabilize the ldg method with the svv operator finally we solve numerically the inviscid fractional burgers equation both with the spectral and the spectral element ldg methods we study systematically the stability and convergence of both methods and determine the effectiveness of each method for different parameters

mindlin plate theory for damage detection source solutions a consideration of the relevant length scales and time scales suggests that mindlin plate theory provides a judicious model for damage detection a systematic investigation of this theory is presented that emphasizes its mixed vector scalar character and analogies with 3d elasticity these analogies lead to the use of helmholtz potentials and to compact statements of the reciprocal theorem and the representation theorem the plate response for a point moment is derived using a direct source specification rather than an indirect specification through boundary conditions solutions are presented for combinations of such point moments doublets that represent respectively a center of bending a center of twist and a center of inplane twist the flexural response due to finite sources such as piezoelectric actuators can be modeled by distributions of centers of bending detailed results are presented for a circular and for a narrow rectangular actuator the far field radiation pattern for an array of equally spaced actuators parallel to a straight boundary is derived the solutions presented for the point moment and the point force constitute the components of a dyadic green s function which is required along with its spatial derivatives for a representation of plate wave scattering by flexural inhomogeneities

new similarity reductions of the boussinesq equation some new similarity reductions of the boussinesq equation which arises in several physical applications including shallow water waves and also is of considerable mathematical interest because it is a soliton equation solvable by inverse scattering are presented these new similarity reductions including some new reductions to the first second and fourth painleve equations cannot be obtained using the standard lie group method for finding group invariant solutions of partial differential equations they are determined using a new and direct method that involves no group theoretical techniques

a new operational matrix for solving fractional order differential equations abstract fractional calculus has been used to model physical and engineering processes that are found to be best described by fractional differential equations for that reason we need a reliable and efficient technique for the solution of fractional differential equations this paper deals with the numerical solution of a class of fractional differential equations the fractional derivatives are described in the caputo sense our main aim is to generalize the legendre operational matrix to the fractional calculus in this approach a truncated legendre series together with the legendre operational matrix of fractional derivatives are used for numerical integration of fractional differential equations the main characteristic behind the approach using this technique is that it reduces such problems to those of solving a system of algebraic equations thus greatly simplifying the problem the method is applied to solve two types of fractional differential equations linear and nonlinear illustrative examples are included to demonstrate the validity and applicability of the presented technique

application of the operational matrix of fractional order legendre functions for solving the time fractional convection diffusion equation the operational matrix of fractional order legendre functions method are considered the fractional order convection diffusion problem is solved the problem can be used extensively in science and engineering as in oil reservoir simulations problems which an initially discontinuous profile is propagated by diffusion and convection in this paper the application of the operational matrix of fractional order legendre functions flfs to solve the time fractional convection diffusion equation has been investigated fractional calculus has been applied to model the engineering and physical processes which are best described with other mathematical tools the time variable of the time fractional convection diffusion equation and its space variable have been approximated by flfs and shifted legendre polynomials respectively the fractional derivatives together with product matrices of flfs are employed to convert the solution of this problem to the solution of a system of algebraic equations

point source representation for laser generated ultrasound the stress free thermal strain corresponding to the temperature rise induced in a target by an incident laser pulse constitutes a volume source of ultrasound in the present work the appropriate point source representation is derived by starting from a general representation theorem for volume sources a formal solution for the double hankel laplace transform of the displacement potentials is obtained for axially symmetric configurations with the point source lying within or on the surface of a half space or a plate the cagniard de hoop technique is used to invert these double transforms for the source on the surface of a half space detailed results are presented for the wave front expansions the displacement along the axis of symmetry and on the surface the directivity pattern and the partition of energy between longitudinal transverse and surface waves for the source within or on the surface of a plate only the epicentral displacement is considered in detail

stable evaluations of fractional derivative of the muntz legendre polynomials and application to fractional differential equations abstract the aim of this paper is to present efficient and stable methods to compute caputo fractional derivative cfd of the muntz legendre polynomials based on three term recurrence relations and gauss jacobi quadrature rules this approach with collocation method at chebyshev gauss lobatto points has been applied for solving linear and nonlinear fractional multi order differential equations fdes described in caputo sense the main characteristic of spectral collocation method is that the problems reduce to linear or nonlinear systems of algebraic equations in this work for the first time we present the new rates of convergence for projection error which are more accurate than the rate presented by shen and wang in shen and wang 2016 moreover we present convergence rate for spectral collocation method for linear fdes with initial value on a finite interval and endpoint singularities also we propose an error analysis for jacobi gauss type quadrature and present a way to accelerate the convergence rate for singular integrands applied in this paper finally the stability and applicability of the numerical approach and convergence analysis is demonstrated by some numerical examples

job search and employment abstract a multistage search method based on fuzzy preference is used to analyze the processes of job search an employment decision based on fuzzy preference results in an exact choice the incorporation of fuzzy interval preference into employment decision however may lead to multiple choices which provides a theoretical justification for the existence of fuzzy supply of labor thus fuzziness in addition to randomness offers an explanation to wage dispersion

infinite dimensional symmetry algebras and an infinite number of conserved quantities of the 2 1 dimensional davey stewartson equation an infinite dimensional symmetry algebra of the davey stewartson equation is explicitly presented it is shown that this algebra is a gauge generalization of the symmetry transformation for the schrodinger equation and that the virasoro algebra appears as the subalgebra an infinite number of conserved quantities associated with the transformations are also obtained

similarity reductions of the kp equation by a direct method basing on a direct method developed by clarkson and kruskal 1989 the kadomtsev petviashvili kp equation has been reduced to three types of 1 1 dimensional partial differential equations which are equivalent to the three types of the similarity reduction equations obtained by the classical lie approach but with different independent variables more arbitrary functions which have been missed by the classical lie approach have been included in the solutions of the kp equation for instance the third type of reduction obtained by the direct method can be divided into three subcases and the third type of solution of the kp equation obtained by the classical lie approach is only a special case of one subcase of the authors results

an algorithm for solving multi term diffusion wave equations of fractional order in this paper an algorithm based on a new modified homotopy perturbation method mhpm is presented to obtain approximate solutions of multi term diffusion wave equations of fractional order to illustrate the method some examples are provided the results show the simplicity and the efficiency of the algorithm

on the infinite dimensional symmetry group of the davey stewartson equations the lie algebra of the group of point transformations leaving the davey stewartson equations dse s invariant is obtained the general element of this algebra depends on four arbitrary functions of time the algebra is shown to have a loop structure a property shared by the symmetry algebras of all known 2 1 dimensional integrable nonlinear equations subalgebras of the symmetry algebra are classified and used to reduce the dse s to various equations involving only two independent variables

application of fuzzy reasoning to precision inserting operation abstract this paper deals with a precision inserting operation for chamferless parts under vague positional information by using approximate reasoning the position of the parts is recognized by introducing two fuzzy sets one is characterized by the membership function of a search area the other is by that of the hole center position the system consists of a scara selective compliance assembly robot arm a force torque sensor and an rcc remote center compliance device the matching degree of two fuzzy sets determines the ranking of search areas the membership function of the hole center position is changed by past information of the precision inserting operation after determining the search area according to the ranking the robot performs the assembly by using the force torque sensor the usefulness in the precision inserting operation is shown by experimental results

a difference scheme for burgers equation in an unbounded domain the numerical solution of the one dimensional burgers equation in an unbounded domain is considered two artificial boundaries are introduced to make the computational domain finite on both artificial boundaries two exact boundary conditions are proposed respectively to reduce the original problem to an initial boundary value problem in a finite computational domain a difference scheme is constructed by the method of reduction of order to solve the problem in the finite computational domain at each time level only a strictly diagonal dominated tridiagonal system of linear algebraic equations needs to be solved it is proved that the difference scheme is uniquely solvable and unconditional convergent with the convergence order 3 2 in time and order 2 in space in an energy norm a numerical example demonstrates the theoretical results

travelling wave solutions to some time space nonlinear evolution equations in this article the modified direct algebraic method has been extended to celebrate the new complex travelling wave solutions of nonlinear evolution equations of fractional order for finding solutions the fractional complex transformation has been implemented to convert nonlinear partial fractional differential equations into nonlinear ordinary differential equations after this the modified direct algebraic method has been applied successfully to construct the complex travelling wave solutions as far as concerned about the applications the nonlinear time space fractional kdv foam drainage and coupled burgers equations of fractional order have been considered

infinitely many symmetries of the davey stewartson equation using a formal series symmetry method for the davey stewartson equation dse we find that there exist two sets of infinitely many formal series symmetries of the dse however different from the kadomtsev petviashvili equation kpe we failed to get infinitely many truncated symmetries only six truncated symmetries can be obtained simply from the formal series symmetries

new exact solutions for some nonlinear differential equations using symbolic computation based on computerized symbolic computation and a new general ansatze a generalized tanh function method for constructing multiple travelling wave solutions of nonlinear evolution equations nees is presented and implemented in a computer algebraic system applying the generalized method with the aid of maple we consider some nees with physics interests as a result we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh function method and other more sophisticated methods more importantly for some equations we also obtain other new and more general solutions at same time the results include kink profile solitary wave solutions bell profile solitary wave solutions periodic wave solutions rational solutions singular solutions and new formal solutions the properties of the new soliton solutions for wbk equations are shown by some figures

numerical doubly periodic solution of the kdv equation with the initial condition via the decomposition method in this paper a scheme is extended to study numerical doubly periodic solutions of the kortweg de vries kdv equation with initial conditions using the adomian decomposition method as a result we obtain the numerical doubly periodic solutions of the kdv equation with initial conditions the numerical doubly periodic solution is compared with the exact doubly periodic solution moreover we analyze the absolute error and relative error between them and also give the contour and density plots of the numerical doubly periodic solutions with two different moduli m 15 78

a reliable modification of adomian decomposition method in this paper we propose a powerful modification of adomian decomposition method that will accelerate the rapid convergence of the series solution the validity of the modified technique is verified through illustrative examples in all cases of differential and integral equations we obtained excellent performance from the modified algorithm the modification could lead to a promising approach for many applications in applied sciences

numerical solutions of coupled burgers equations with time and space fractional derivatives in this paper by introducing the fractional derivative in the sense of caputo the adomian decomposition method is directly extended to study the coupled burgers equations with time and space fractional derivatives as a result the realistic numerical solutions are obtained in a form of rapidly convergent series with easily computable components the figures show the effectiveness and good accuracy of the proposed method

analytical and numerical aspects of certain nonlinear evolution equations 1v numerical modified korteweg de vries equation various numerical methods are used in order to approximate the korteweg de vries equation namely i zabusky kruskal scheme ii hopscotch method iii a scheme due to goda iv a proposed local scheme v a proposed global scheme vi a scheme suggested by kruskal vii split step fourier method by tappert viii an improved split step fourier method and ix pseudospectral method by fornberg and whitham comparisons between our proposed scheme which is developed using notions of the inverse scattering transform and the other utilized schemes are obtained

numerical solutions for fractional kdv burgers equation by adomian decomposition method abstract based on the symbolic computation system maple adomian decomposition method developed for differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional kdv burgers equation the fractional derivatives are described in the caputo sense according to my knowledge this paper represents the first available numerical solutions of the nonlinear fractional kdv burgers equation with time and space fractional derivatives finally the solutions of our model equation are calculated in the form of convergent series with easily computable components

painleve analysis and backlund transformation in the kuramoto sivashinsky equation the authors apply the painleve test to the kuramoto sivashinsky nonlinear partial differential equation which describes many interesting fluid motions the equation passes the test in a weak sense although the painleve analysis does not yield the general solution they perform the backlund transformation in order to obtain new particular solutions the authors find explicitly all the solutions of the set of equations which define the painleve backlund transformation they reduce to only one type namely the already known kink shaped solitary wave