spurious poles in pade approximation in the theory of pade approximation locally uniform convergence has been proved only for special classes of functions for much larger classes convergence in capacity has been shown to hold true the reason for one type of convergence to hold true but the other one not can be found in poles of the approximants that may occur apparently anywhere in the complex plane because of their unwanted nature and since they do not correspond to singularities of the function f to be approximated these poles are called spurious the denominators of pade approximants satisfy orthogonality relations and consequently the location and distribution of spurious poles depend on properties of the orthogonality relations in the present paper the possibility of spurious poles is studied from the perspective of these orthogonal relations

discrete exact solutions to some nonlinear differential difference equations via the g g expansion method we extended the g g expansion method to two well known nonlinear differential difference equations the discrete nonlinear schrodinger equation and the toda lattice equation for constructing traveling wave solutions discrete soliton and periodic wave solutions with more arbitrary parameters as well as discrete rational wave solutions are revealed it seems that the utilized method can provide highly accurate discrete exact solutions to nddes arising in applied mathematical and physical sciences

adm pade technique for the nonlinear lattice equations adm pade technique is a combination of adomian decomposition method adm and pade approximants we solve two nonlinear lattice equations using the technique which gives the approximate solution with higher accuracy and faster convergence rate than using adm alone bell shaped solitary solution of belov chaltikian bc lattice and kink shaped solitary solution of the nonlinear self dual network equations sdnes are presented comparisons are made between approximate solutions and exact solutions to illustrate the validity and the great potential of the technique

some new results on the blaszak marciniak lattice backlund transformation and nonlinear superposition formula the so called blaszak marciniak lattice is considered by the dependent variable transformation the blaszak marciniak lattice is transformed into a quart linear form by introducing an auxiliary variable we further transform it into the bilinear form a corresponding backlund transformation is obtained furthermore a nonlinear superposition formula is proved rigorously as an application of the obtained results soliton solutions are derived

new integrable systems related to the relativistic toda lattice the bi hamiltonian structure of the relativistic toda lattice is exploited to introduce some new integrable lattice systems their integrable discretizations are obtained by means of the general procedure proposed recently by the author backlund transformations between the new systems and the relativistic toda lattice in both the continuous and discrete time formulations are established

algebro geometric analogues of donaldson s polynomials donaldson 5 has introduced polynomials on the second homology of any simply connected closed four manifold m with b odd at least 3 which up to are invariant under orientation preserving diffeomorphisms for every c ibm there is a polynomial 7c m syma h2 s where d c 4c z2 b 1 to define it one considers j c the set which is in a natural way a manifold of gauge equivalence classes of connections on the su 2 bundle on m with c2 c antiself dual with respect to a generic metric on m there is a natural map h2 m h2 j c namely slant product with 88 where p is the universal so 3 principal bundle on m x j c one way of defining 7c m 10 is to construct a compactification of r xc carrying a fundamental class xc one proves that extends to a map h2 m h2 xc then one defines

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

the linear quadratic regulator for periodic hybrid systems abstract the main objective of this paper is to characterize feedback control laws that are optimal with respect to a quadratic cost functional in the framework of linear hybrid systems undergoing time driven periodic jumps namely the so called hybrid linear quadratic regulator lqr problem the optimal solution to the hybrid lqr problem is determined both in the case of finite horizon and infinite horizon optimal control problems by introducing a hybrid periodic extension of the classic differential and difference riccati equations thus leading to the notion of monodromy riccati equation interestingly due to the periodic nature of the discrete time events the computation of the optimal feedback hinges upon the solution of a differential rather than algebraic riccati equation also in the infinite horizon case hence yielding a time varying periodic control law necessary and sufficient conditions that ensure asymptotic stability of the closed loop system are provided and discussed in detail in the case of infinite horizon optimal control problems

stabilization of switched linear systems in this note we study the stabilization problem of systems that switch among a finite set of controllable linear systems with arbitrary switching frequency for both cases of known and unknown switching functions feedback laws are designed to achieve exponential stability for the later case a method combining on line adaptive estimation and feedback stabilization is developed in the controller design

the effect of the order of nonlinear dispersive equation on the compact and noncompact solutions the effect of the order of nonlinear dispersive partial differential equation on the compact and noncompact solutions is studied in this paper two variants of the kdv equation of odd orders are examined our analysis reveals that the physical nature of these nonlinear kdv type of equations are different two distinct sets of general formulas for each type of variants are performed to present a fairly complete understanding of the compact and noncompact structures

brief paper state feedback stabilization of linear impulsive systems we address the fundamental problem of state feedback stabilization for a class of linear impulsive systems featuring arbitrarily spaced impulse times and possibly singular state transition matrices specifically we show that a strong reachability property enables a state feedback law to be constructed that yields a uniformly exponentially stable closed loop system the approach adopts a receding horizon strategy involving a weighted reachability gramian in a manner reminiscent of well known results for time varying linear systems for both continuous and discrete time cases

compact structures for variants of the generalized kdv and the generalized kp equations in this paper we discuss mathematical variants in higher dimensions of the generalized kdv and the generalized kp equations it is shown that the focusing branches of these variants exhibit compactons solitons with finite wavelength whereas the defocusing branches support solitary patterns solutions with infinite slopes or cusps the compact and the noncompact dispersive structures are examined in a general way

compactons and solitary patterns structures for variants of the kdv and the kp equations in this paper we discuss mathematical variants in higher dimensions of the kdv and the kp equations it is shown that the focusing branches of these variants exhibit compactons solitons with finite wavelength whereas the defocusing branches support solitary patterns solutions with infinite slopes or cusps the study presents a fairly complete understanding of the compact and noncompact dispersive structures

a computational approach to soliton solutions of the kadomtsev petviashvili equation in this paper we present a computational approach to develop soliton solutions of the nonlinear kadomtsev petviashvili equation our approach rests mainly on the adomian decomposition method to include few components of the decomposition series the proposed framework is presented in a general way so that it can be used in nonlinear evolution equations of the same type numerical examples are tested to illustrate the proposed scheme

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

the sine cosine and the tanh methods reliable tools for analytic treatment of nonlinear dispersive equations the sine cosine method and the tanh method are used for analytic treatment of nonlinear dispersive equations nonlinear variants of boussinesq equation are used as vehicles to show the strength of these methods solutions of distinct physical structures solitons compactons solitary patterns solutions and periodic solutions are formally derived the results show that the change in physical structures of the obtained solutions depends mainly on exponents and on the coefficients of the derivatives involved

disturbance decoupling in hybrid linear systems with state jumps this work investigates the problem of making the output of a hybrid linear system totally insensitive to a disturbance input while attaining global asymptotic stability of the compensated hybrid dynamics in the presence of possibly nonuniformly spaced state jumps meeting the only condition that the minimum time between two consecutive occurrences is no smaller than a given positive real constant both existential and constructive necessary and sufficient conditions for solvability of the problem addressed are proven

stability analysis of systems with impulse effects the authors establish conditions for the uniform stability and the uniform asymptotic stability of equilibria of systems with impulse effects described by systems of nonlinear time varying ordinary differential equations under mild additional assumptions these sufficient conditions turn out to be necessary as well for the case of time invariant systems with impulse effects described by nonlinear ordinary differential equations the above results are used to establish conditions under which the uniform asymptotic stability of equilibria can be deduced from the linearizations of such systems

h control of multirate sampled data systems a state space approach a state space solution of the h control problem for periodic multirate sampled data systems is presented the solution is characterized in terms of a pair of discrete algebraic riccati equations with a set of associated matrix positive definiteness conditions and coupling criteria the solution is derived using two different approaches in the first approach the solution is obtained by discretizing two coupled periodic riccati equations with jumps which characterize the h optimal controller the second approach is based on the lifting technique the h optimal controller for a lifted representation of the multirate system is characterized by a two riccati equation solution in which the so called causality constraint is represented by a set of positive definiteness conditions and coupling criteria

brief paper reachability and observability of linear impulsive systems linear impulsive systems constitute a class of hybrid systems in which the state propagates according to linear continuous time dynamics except for a countable set of times at which the state can change instantaneously while in general these impulsive effects can be time driven and or event driven here we focus our attention on the time driven case for this class of systems we address the fundamental concepts of reachability and observability in particular we present a geometric characterization of the reachable and unobservable sets in terms of invariant subspaces and provide algorithms for their construction

r matrix approach to lattice integrable systems an r matrix formalism is applied to the construction of the integrable lattice systems and their bi hamiltonian structure miura like gauge transformations between the hierarchies are also investigated in the end the ladder of linear maps between generated hierarchies is established and described

belov chaltikian and blaszak marciniak lattice equations recursion operators and factorization a systematic investigation on the construction of recursion operators for partial differential difference equations pddes with two independent variables one continuous and one discrete using its generalized symmetries is presented also it is explained how to factorize the obtained recursion operators the applicability of the above procedure have been illustrated for the relativistic toda rt belov chaltikian bc and blaszak marciniak bm lattice equations and shown that the former two lattice equations admit 2 2 matrix recursion operators while the latter one possesses a 3 3 matrix recursion operator furthermore the constructed recursion operators can be written as a factor of 2 distinct invertible matrix operators in each of the lattice equations it is also proved explicitly that the factorized operators are hamiltonian and hence rt bc and bm lattice equations are bi hamiltonian systems

a backlund transformation and nonlinear superposition formula for the belov chaltikian lattice the so called belov chaltikian lattice is considered by the dependent variable transformation the belov chaltikian lattice is transformed into a trilinear form by introducing an auxiliary variable we further transform it into the bilinear form a corresponding backlund transformation for it is obtained furthermore a nonlinear superposition formula is proved rigorously as an application of the obtained results soliton solutions are derived

an application of the modified adomian decomposition method for n 1 dimensional sine gordon field abstract based upon the modified adomian decomposition method a scheme is developed to obtain approximate jacobi elliptic function solutions of the n 1 dimensional sine gordon field with initial conditions as a result we derive the approximate solution and exact jacobi elliptic function solution of the n 1 dimensional sine gordon field with initial conditions moreover the approximate solution is compared with the exact solution with n 2 and with different modulus k 0 25 0 5 and 1

backlund transformation and its superposition principle of a blaszak marciniak four field lattice a four field lattice furnished by blaszak and marciniak is transformed into bilinear form upon introducing two auxiliary independent variables a backlund transformation in bilinear form is found for the lattice and the corresponding nonlinear superposition formula is rigorously established as a consequence soliton solutions to the lattice are derived

a modified adomian method for system of nonlinear differential equations in this paper a modified adomian method is introduced to solve some systems of nonlinear differential equations the method can be mechanized in maple and a procedure is written to solve the approximate analytic solution of the systems some examples will be presented to illustrate the effectiveness of the method and the procedure a comparison between the program and the original adomian method s program is drawn

the ablowitz ladik lattice system by means of the extended g g expansion method abstract we analyzed the ablowitz ladik lattice system by using the extended g g expansion method further discrete soliton and periodic wave solutions with more arbitrary parameters are obtained we observed that some previously known results can be recovered by assigning special values to the arbitrary parameters

brief paper feedback reversibility and reachability of linear impulsive systems for a linear impulsive system the set of states that are reachable from the origin when the initial time impulse times and final time are fixed is contained in an invariant subspace determined by the system data it is known that reversibility of the system is sufficient to yield for a specified initial time the existence of some impulse time set and final time for which the reachable set equals the invariant subspace in this paper we relax the reversibility requirement and present a condition that is necessary as well as sufficient under which this property holds this new condition involves the property of achieving reversibility via feedback and admits an explicit geometric characterization moreover this feedback reversibility property only needs to hold for the subsystem defined as the full system restricted to the invariant subspace we further show that feedback reversibility of the restricted system ensures that the reachable set equals the invariant subspace for almost any impulse time set and final time for which the number of impulse times contained in the underlying time interval exceeds a lower bound

approximate jacobi elliptic function solutions of the modified kdv equation via the decomposition method the scheme is developed to obtain approximate jacobi elliptic function solutions of the modified kdv equation with initial conditions via the adomian decomposition method as consequence we derive the approximate solution and exact jacobi elliptic function solutions of the modified kdv equation with initial conditions the approximate solution is compared with the exact solution moreover we analyze the absolute error and relative error and give the contour and density plots of the approximate jacobi elliptic function solutions with different modulus m 0 25 0 5 1

numerical study of modified adomian s method applied to burgers equation the application of adomian s decomposition method to partial differential equations when the exact solution is not reached demands the use of truncated series but the solution s series may have small convergence radius and the truncated series may be inaccurate in many regions in order to enlarge the convergence domain of the truncated series pade approximants pas to the adomian s series solution have been tested and applied to partial and ordinary differential equations with good results in this paper pas both in x and t directions applied to the truncated series solution given by adomian s decomposition technique for burgers equation are tested numerical and graphical illustrations show that this technique can improve the accuracy and enlarge the domain of convergence of the solution it is also shown in this paper that the application of adomian s method to the ordinary differential equations set arising from the discretization of the spatial derivatives by finite differences the so called method of lines may reduce the convergence domain of the solution s series

similarity reduction generalized symmetries and integrability of belov chaltikian and blaszak marciniak lattice equations the lie point symmetries of belov chaltikian bc and blaszak marciniak bm lattice equations is derived using the symmetries similarity reduction for both bc and bm lattice equations is obtained and show that each of the reduced equation possesses lax representation and satisfies the singularity confinement criteria a discrete version of the painleve property indicating their integrability two particular solutions of both the reduced equations are given explicitly a systematic investigation for nonclassical symmetries of bc and bm lattice equations is carried out further a sequence of conserved densities and generalized symmetries of both bc and bm lattice equation are derived explicitly the existence of a sequence of such symmetries is a predictor for integrability

a new fractional order soliton equation hierarchy and its integrable coupling system a fractional order soliton equation hierarchy is presented which is a new liouville integrable hierarchy and possesses bi hamiltonian structure finally we obtain a integrable coupling system of this fractional order soliton equation hierarchy by applying a upper triangular matrix of lie algebras

output regulation by error dynamic feedback in hybrid systems with periodic state jumps abstract this work deals with output regulation in multivariable hybrid systems featuring a continuous time linear dynamics periodically affected by instantaneous changes of the state more precisely given a hybrid linear plant and a hybrid linear exogenous system with periodic state jumps the problem consists in finding a hybrid feedback regulator with the same characteristics achieving global asymptotic stability of the closed loop dynamics and asymptotic tracking of the reference generated by the exogenous system for all the initial states starting from a general necessary and sufficient condition for the existence of a solution the discussion leads to a more specific sufficient condition which outlines the computational framework for a straightforward synthesis of the compensator the internal model principle is shown to hold in a more general formulation than the original one adapted to the hybrid systems considered a numerical example is worked out with the aim of illustrating how to implement the devised technique the geometric approach is the key methodology in attaining these results

solutions of compact and noncompact structures for nonlinear klein gordon type equation the focusing and the defocusing branches of nonlinear klein gordon type equation kg n n are considered a framework is implemented to show that the first model exhibits compactons solitons that do not have exponential tails whereas the second model demonstrates solitary patterns solutions the two variants of kg n n equation will be examined in one and higher dimensions general formulas will be developed to present a fairly complete understanding of the solutions of compact and noncompact structures

a reliable treatment of the physical structure for the nonlinear equation k m n in this work the nonlinear equation k m n is studied for all possible values of m and n we show that this equation may exhibit compactons solitons or periodic solutions the analysis reveals the change of the physical structure of the solutions as a result of the change of m and n

variants of the two dimensional boussinesq equation with compactons solitons and periodic solutions variants of the two dimensional boussinesq equation with positive and negative exponents are studied the sine cosine ansatz is fruitfully used to carry out the analysis exact solutions of different physical structures compactons solitary patterns solitons and periodic solutions are obtained the quantitative change in the physical structure of the solutions is shown to depend mainly on the exponent of the wave function u x t and on the ratio a b of the derivatives of u x t

an analytic study of compacton solutions for variants of kuramoto sivashinsky equation in this paper two mathematical variants of kuramoto sivashinsky equation are examined a framework is developed for studying these variants in one and higher dimensions two distinct sets of general formulae for each variant are developed compactons solitons with compact support and noncompact dispersive structures are formally established

solitary wave solutions for the general kdv equation by adomian decomposition method in recent publications chaos solitons fractals 12 2001 2283 int j appl math 3 4 2000 361 we have dealt with the numerical solutions of the korteweg de vries kdv and modified korteweg de vries mkdv equations we extend this study to a more general nonlinear equation which is the general korteweg de vries gkdv equation in which the previous studies is a special case of it the method applied here is adomian decomposition method which has been developed by george adomian solving frontier problems of physics the decomposition method kluwer academic publishers boston ma 1994 numerical examples are tested to illustrate the pertinent feature of the proposed algorithm

general compactons solutions for the focusing branch of the nonlinear dispersive k n n equations in higher dimensional spaces in this paper we will study the focusing branch of the genuinely nonlinear dispersive k n n equation that exhibits compactons solitons with finite wavelengths the equation will be studied in one two and three dimensional spaces general formulas for compactons solutions are developed for all positive integers n n 1 two sets of entirely new formulas one set produces compactons for even integers n whereas the second set produces compactons and anticompactons for odd integers n n 1 are established

numerical simulation of kadomtsev petviashvili benjamin bona mahony equations using finite difference method in this paper the finite difference method is employed to solve kadomtsev petviashvili benjamin bona mahony ii kp bbm ii partial differential equations the time and space variable are discretized by the crank nicholson method and the central difference scheme respectively the consistence and stability are also proved some examples are investigated to verify the efficiency of the present method

variants of the generalized kdv equation with compact and noncompact structures abstract in this paper nonlinear dispersive variants of the generalized kdv equation are investigated the compact and the noncompact physical structures are studied two general formulas for the focusing branch and the defocusing branch that are of substantial interest are formally derived

analytical approximations and pade approximants for volterra s population model in this paper an analytic approximation for volterra s model for population growth of a species in a closed system is presented the nonlinear integro differential model includes an integral term that characterizes accumulated toxicity on the species in addition to the terms of the logistic equation the series solution method and the decomposition method are implemented independently to the model and to a related ode the pade approximants that often show superior performance over series approximations are effectively used in the analysis to capture the essential behavior of the population u t of identical individuals

on the 1 curve conjecture of friedman and morgan we will prove that every differentiably embedded sphere with self intersection 1 in a simply connected algebraic surface withp g 0 is homologous to an algebraic class if the surface has a minimal model with picard number 1 or k min contains a smooth curve and eitherp g ork min 2 is even then every such sphere is homologous to a 1 curve as conjectured by friedman and morgan

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

h sub infinity control and filtering for sampled data systems h sub infinity control and filtering problems for sampled data systems are studied necessary and sufficient conditions are obtained for the existence of controllers and filters that satisfy a specified h sub infinity performance bound when these conditions hold explicit formulas for a controller and a filter satisfying the h sub infinity performance bound are also given

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

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

a construction of compact and noncompact solutions for nonlinear dispersive equations of even order a construction of compact and noncompact solutions for nonlinear dispersive partial differential equations of even order is considered two model equations of even orders k 4 are adopted to carry out this study the analysis reveals the presence of distinct roots of different indices that play a significant role in the solutions

controllability and stabilizability of switched linear systems in this paper we study the conjecture made in ieee trans automat control 47 8 2002 1401 concerning the existence of basic switching sequence for switched systems and give it an affirmative answer and a construction method this paper proves that for switched linear system there exists a switching sequence such that the controllable state set of this switching sequence is equal to the controllable state set of the system hence the controllability can be realized by using only one switching sequence then the result is extended to the systems with time delay in controls furthermore we define the stabilizability of switched linear systems and based on certain transformation of state coordinate we give a necessary and sufficient condition for the stabilizability two examples are presented to illustrate the obtained results

solutions of the kp equation associated to rank three commuting differential operators over a singular elliptic curve abstract we give a method for finding explicit solutions of the kadomtsev petviashvili kp equation which are associated to rank three commuting ordinary differential operators explicit formulae for the coefficients of rank three commuting differential operators are used to reduce the kp equation to a nonlinear partial differential equation in only two variables this equation which is obtained in a similar way to the rank two krichever novikov kn equation is easier to solve than kp and some solutions are given

the modified decomposition method and pade approximants for solving the thomas fermi equation in this paper we propose a new approach to develop a nonperturbative approximate solution for the thomas fermi equation this approach rests on the recently developed modification of the adomian decomposition method the initial slope of the thomas fermi potential y 0 is computed by converting the obtained series solution into several diagonal pade approximants the proposed scheme is presented in a general way so that it can be used in applied sciences

a class of nonlinear fourth order variant of a generalized camassa holm equation with compact and noncompact solutions abstract in this paper we study a class of nonlinear fourth order analogue of a generalized camassa holm equation it is shown that this class gives compactons conventional solitons solitary patterns and periodic solutions it is also found that the qualitative change in the physical structure of solutions depends mainly on the exponent of the wave function u x t positive or negative and on the coefficient of u n as well

a study on nonlinear dispersive partial differential equations of compact and noncompact solutions in this paper we study two genuinely nonlinear dispersive partial differential equations in one and higher dimensional spaces we show that the focusing branch and the defocusing branch of these equations each leads to a different physical structure in addition we develop general solutions of compact and noncompact support which are not obtainable through classic techniques

compactons structures for fifth order kdv like equations in higher dimensions in this paper we study a variant of the fifth order kdv equation fkdv that exhibits compactons solitons with finite wave lengths the work formally shows how to construct compact dispersive structures in higher dimensions two sets of general formulas for compactons solutions that are of substantial interest are developed for this variant fk n n for all positive integers n n 1