the cauchy problem for the generalized imbq equation in ws p rn in this paper the existence and the uniqueness of the global strong solution and the global classical solution for the cauchy problem of the multidimensional generalized imbq equation are proved the nonexistence of the global solution for the cauchy problem of the generalized imbq equation is discussed

local and global existence of solutions for the cauchy problem of a generalized boussinesq equation abstract we consider the local and global existence of solutions for a generalized boussinesq equation u t t u x x u x x x x u k 1 x x 0 k 4 with initial data in some homogenous besov type space

existence and nonexistence of global solutions for a class of nonlinear wave equations of higher order abstract in this paper we investigate the existence and uniqueness of the solution to the cauchy problem for a class of nonlinear wave equations of higher order and prove the existence and nonexistence of global solutions to this problem by a potential well method

analysis of ciarlet raviart mixed finite element methods for solving damped boussinesq equation abstract in this paper we consider the numerical solution of damped boussinesq equation using ciarlet raviart mixed finite element method an implicit finite difference scheme is used for the time discretization a priori error estimates are analyzed and stability analysis of the method is shown we obtain an optimal error estimate in l 2 norm with quadratic or higher order element for both semi and fully discrete finite element approximations finally numerical examples are given to verify the theoretical results

blow up and scattering of solution for a generalized boussinesq equation in this paper we consider the cauchy problem for a class of boussinesq equation we obtain the existence and uniqueness of the local solutions for a class of nonlinearity of the perturbation blow up solutions are obtained furthermore the global existence and nonlinear scattering for small amplitude solutions are established

global existence and asymptotic behavior of solution for the sixth order boussinesq equation with damped term abstract we investigate the small data cauchy problem for the sixth order boussinesq equation with damped term the decay estimates of solutions to the corresponding linear equation are given by using the dyadic decomposition and some properties of bessel functions then we prove the global existence and asymptotic of the small amplitude solution in the time weighted sobolev space by the contraction mapping principle

on computing rational gauss chebyshev quadrature formulas we provide an algorithm to compute the nodes and weights for gauss chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary real poles outside 1 1 contrary to existing rational quadrature formulas the computational effort is very low even for extremely high degrees and under certain conditions on the poles it can be shown that the complexity is of order o n this method is based on the derivation of explicit expressions for chebyshev orthogonal rational functions which are thus far the only examples of explicitly known orthogonal rational functions on 1 1 with arbitrary real poles outside this interval

the dynamics of a nonlinear wave equation we consider a wave equation in a bounded domain with linear dissipation and with a nonlinear source term we give characterizations of all the solutions with respect to their qualitative properties globality boundedness nonglobality blow up and convergence to equilibria

a new n 6 superconformal algebra in this paper we construct a newn 6 superconformal algebra which extends the virasoro algebra by theso 6 current algebra by 6 odd primary fields of conformal weight 3 2 and by 10 odd primary fields of conformal weight 1 2 the commutation relations of this algebra which we will refer to asck 6 are represented by short distance operator product expansions ope we constructck 6 as a subalgebra of theso 6 superconformal algebra k6 thus giving it a natural representation as first order differential operators on the circle withn 6 extended symmetry we show thatck 6 has no nontrivial central extensions

on potential wells and vacuum isolating of solutions for semilinear wave equations abstract in this paper we study the initial boundary value problem of semilinear wave equations u tt u u p 1 u x t 0 u x 0 u 0 x u t x 0 u 1 x x u x t 0 x t 0 where r n is a bounded domain 1 1 n 2 n 2 for n 3 first by using a new method we introduce a family of potential wells which include the known potential well as a special case then by using it we obtain some new existence theorems of global solutions and prove that for any e 0 d d is the depth of the known potential well all solutions with initial energy e 0 satisfying 0 h 0 1

kawahara dynamics in dispersive media abstract in a previous paper it was shown that in the long wave limit the water wave problem without surface tension can be described approximately by two decoupled kdv equations here we study a model problem and prove that in a degenerate case which occurs for the water wave problem with surface tension and near other codimension two points at which the coefficient in front of the leading order dispersive term in the equation of motion vanishes the long wave limit can be rigorously approximated by two decoupled kawahara equations

potential method applied to boussinesq equation in this paper a solution of the nonlinear boussinesq equation is presented using the potential similarity transformation method the equation is first written in a conserved form a potential function is then assumed reducing it to a system of equations which is further solved through the group transformation method new transformations are found

an extended relation between orthogonal rational functions on the unit circle and the interval 1 1 abstract the relation between orthogonal polynomials on the unit circle and the interval has been given by szeg in this paper we generalize this relation to orthogonal rational functions with prescribed complex poles as an application we obtain explicit expressions for the orthogonal rational functions with respect to the weight functions 1 cos on the unit circle respectively 1 x 1 x 1 2 on the interval and use one of them to illustrate the relation

rational interpolation ii quadrature and convergence abstract consider an n th rational interpolatory quadrature rule j n f j 1 n j f x j to approximate integrals of the form j f 1 1 f x d x where is a possibly complex bounded measure with infinite support on the interval 1 1 first we discuss the connection of j n f with certain rational interpolatory quadratures on the complex unit circle to approximate integrals of the form f e i d c where c is a possibly complex bounded measure with infinite support on next we provide conditions to ensure the convergence of j n f to j f for n tending to infinity finally an upper bound for the error on the n th approximation and an estimate for the rate of convergence is provided

strong instability of solitary wave solutions of a generalized boussinesq equation abstract in this paper we prove the strong instability of solitary wave solutions with small speed of propagation for a generalized boussinesq equation

a connection between quadrature formulas on the unit circle and the interval 1 1 abstract we establish a relation between gauss quadrature formulas on the interval 1 1 that approximate integrals of the form i f 1 1 f x x d x and szeg quadrature formulas on the unit circle of the complex plane that approximate integrals of the form i f f e i d the weight x is positive on 1 1 while the weight is positive on it is shown that if cos sin then there is an intimate relation between the gauss and szeg quadrature formulas moreover as a side result we also obtain an easy derivation for relations between orthogonal polynomials with respect to x and orthogonal szeg polynomials with respect to inclusion of gauss lobatto and gauss radau formulas is natural

solutions of the boussinesq equation on a periodic domain abstract the existence and the uniqueness of solutions for a linear feedback controlled boussinesq equation on a periodic domain are studied the continuous dependence of the solution on initial data is also proved the proof is based on conservation laws for the boussinesq equation

small amplitude solutions of the generalized imbq equation in this paper the global existence of small amplitude solution for the cauchy problem of the multidimensional generalized imbq equation is proved moreover we obtain a nonlinear scattering result of the cauchy problem of the imbq equation for small initial data

rational gauss chebyshev quadrature formulas for complex poles outside 1 1 in this paper we provide an extension of the chebyshev orthogonal rational functions with arbitrary real poles outside 1 1 to arbitrary complex poles outside 1 1 the zeros of these orthogonal rational functions are not necessarily real anymore by using the related para orthogonal functions however we obtain an expression for the nodes and weights for rational gauss chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary complex poles outside 1 1

new solutions for solving boussinesq equation via potential symmetries method this work deals with the boussinesq equation that describes the propagation of the solitary waves with small amplitude on the surface of shallow water firstly the equation is written in a conserved form a potential function is then assumed reducing it to a system of partial differential equations the lie group method has been applied for determining symmetry reductions of the system of partial differential equations the solution of the problem by means of lie group method reduces the number of independent variables in the given partial differential equation by one leading to nonlinear ordinary differential equations the resulting non linear ordinary differential equations are then solved numerically using matlap package

decay and scattering of small solutions of a generalized boussinesq equation abstract we study the long time behavior of small solutions of the initial value problem for a generalized boussinesq equation we obtain a lower bound for the degrees of nonlinearity which allows us to establish a nonlinear scattering result for small perturbations that is the small solutions of the nonlinear problem behave asymptotically like the solution of the associated linear problem under certain hypotheses we can construct a scattering operator for the boussinesq equation which carries a neighborhood of 0 in the energy space x into x

a generalized eigenvalue problem for quasi orthogonal rational functions in general the zeros of an orthogonal rational function orf on a subset of the real line with poles among alpha 1 ldots alpha n subset mathbb c 0 cup infty are not all real unless alpha n is real and hence they are not suitable to construct a rational gaussian quadrature rule rgq for this reason the zeros of a so called quasi orf or a so called para orf are used instead these zeros depend on one single parameter tau in mathbb c cup infty which can always be chosen in such a way that the zeros are all real and simple in this paper we provide a generalized eigenvalue problem to compute the zeros of a quasi orf and the corresponding weights in the rgq first we study the connection between quasi orfs para orfs and orfs next a condition is given for the parameter so that the zeros are all real and simple finally some illustrative and numerical examples are given

rational szego quadratures associated with chebyshev weight functions in this paper we characterize rational szeg o quadrature formulas associated with chebyshev weight functions by giving explicit expressions for the corresponding para orthogonal rational functions and weights in the quadratures as an application we give characterizations for szeg o quadrature formulas associated with rational modifications of chebyshev weight functions some numerical experiments are finally presented

global solution for a generalized boussinesq equation this paper considers the existence and uniqueness of the solution to the cauchy problem for a class of boussinesq equation proves the global existence and finite time blowup of the solution to the problem by the potential well method

global existence of smooth solutions and stability of solitary waves for a generalized boussinesq equation certain generalizations of one of the classical boussinesq type equations u tt u xx u 2 u xx xx are considered it is shown that the initial value problem for this type of equation is always locally well posed it is also determined that the special solitary wave solutions of these equations are nonlinearly stable for a range of their phase speeds these two facts lead to the conclusion that initial data lying relatively close to a stable solitary wave evolves into a global solution of these equations this contrasts with the results of blow up obtained recently by kalantarov and ladyzhenskaya for the same type of equation and casts additional light upon the results for the original version of this class of equations obtained via inverse scattering theory by deift tomei and trubowitz