collocation methods for the solution of von karman dynamic non linear plate systems the von karman nonlinear dynamic partial differential system over rectangular domains is considered and numerically solved using both the chebyshev collocation and legendre collocation methods for the spatial discretization and the implicit newmark scheme combined with a non linear fixed point algorithm for the temporal discretization as the system is non linear involving operators of different orders different timescales and may contain initial boundary incompatible conditions at the domain s corners it is our aim to highlight some of the difficulties inherent in its numerical treatment using collocation methods we begin by examining the chebyshev collocation scheme considered in comput meth appl mech engrg 193 6 8 2004 575 in that work filtering was used to stabilize the full von karman system however the source of the instability was not discussed we first show that ic bc incompatibilities are not the culprits and demonstrate empirically that the source of the instability was the numerical treatment of the linear cross derivative terms found in the in plane equations we prove mathematically that although the continuous linear system is well posed the chebyshev collocation solution of problems involving cross derivatives and second order time derivatives is unstable instead of adding sufficient filtering to counter the energy growth due to the linear terms we employ the legendre collocation method we show empirically and prove that the legendre collocation scheme for the linear system has the necessary characteristics to remain stable nevertheless the collocation treatment of the non linear terms still causes the solution to be unstable at long time we thus return to advocating a filtering solution but in this case only filtering the non linear terms to compensate for the inherent aliasing error due to our collocation treatment of these terms we conclude by comparing the results of filtered chebyshev collocation solution non linear terms filtered legendre collocation solution and a simplified von karman solution omitting the inertial terms in the in plane equations as presented in loc cit

upper bounds on wavepacket spreading for random jacobi matrices a method is presented for proving upper bounds on the moments of the position operator when the dynamics of quantum wavepackets is governed by a random possibly correlated jacobi matrix as an application one obtains sharp upper bounds on the diffusion exponents for random polymer models coinciding with the lower bounds obtained in a prior work the second application is an elementary argument not using multiscale analysis or the aizenman molchanov method showing that under the condition of uniformly positive lyapunov exponents the moments of the position operator grow at most logarithmically in time

n soliton solutions for a 2 1 dimensional breaking soliton equation with self consistent sources abstract a 2 1 dimensional breaking soliton equation with self consistent sources 2 1 dbsescs is derived the bilinear form of it is obtained and the n soliton solutions are worked out by means of the hirota method and wronskian technique respectively by making use of the laplace expansion formula a simple method is presented to treat the nonlinear term in the bilinear equation and finish the wronskian verification the dynamics and source effects are investigated

stability and vibration of thick laminated composite sector plates this study presents a simple analytical formulation for the eigenvalue problem of buckling and free vibration analysis of shear deformable laminated sector plates made up of cylindrically orthotropic layers the non axisymmetric formulation in cylindrical coordinates is discretized in space domain in terms of two dimensional chebyshev polynomials several combinations of simply supported clamped and free edge conditions are considered convergence study has been carried out and the obtained results are compared with the results of laminated square plates and isotropic sector plates available in literature extensive results pertaining to critical buckling loads and natural frequencies are presented effects of boundary conditions number of layers moduli ratio rotary and in plane inertia plate thickness sector angle and annularity are studied

the fibonacci hamiltonian we consider the fibonacci hamiltonian the central model in the study of electronic properties of one dimensional quasicrystals and establish relations between its spectrum and spectral characteristics namely the optimal holder exponent of the integrated density of states the dimension of the density of states measure the dimension of the spectrum and the upper transport exponent and the dynamical properties of the fibonacci trace map such as dimensional characteristics of the non wandering hyperbolic set and its measure of maximal entropy as well as other equilibrium measures topological entropy multipliers of periodic orbits we also exhibit a connection between the spectral quantities and the thermodynamic pressure function as a result a detailed description of the spectral properties for all values of the coupling constant is obtained in contrast to all previous quantitative results which could be established only in the regime of small or large coupling in particular we show that the spectrum of this operator is a dynamically defined cantor set and that the density of states measure is exact dimensional this implies that all standard fractal dimensions coincide in each case we show that all the gaps of the spectrum allowed by the gap labeling theorem are open for all values of the coupling constant also we establish strict inequalities between the four spectral characteristics in question and provide the exact large coupling asymptotics of the dimension of the density of states measure for the other three quantities the large coupling asymptotics were known before

a new constrained mkp hierarchy and the generalized darboux transformation for the mkp equation with self consistent sources abstract the mkp equation with self consistent sources mkpescs is treated in the framework of the constrained mkp hierarchy we introduce a new constrained mkp hierarchy which may be viewed as the stationary hierarchy of the mkp hierarchy with self consistent sources this offers a natural way to obtain the lax representation for the mkpescs based on the conjugate lax pairs we construct the generalized darboux transformation with arbitrary functions in time t for the mkpescs which in contrast with the darboux transformation for the mkp equation provides a nonauto backlund transformation between two mkpescss with different degrees the formula for n times repeated generalized darboux transformation is proposed and enables us to find the rational solutions including the lump solutions soliton solutions and the solutions of breather type of the mkpescs

vibration of annular sector plates from three dimensional analysis accurate three dimensional elasticity solutions are presented for the free vibration analysis of annular sector plates with arbitrary but continuous boundary conditions the ritz procedure is used to minimize the integral energy functional which is formulated in a cylindrical polar coordinate system in the derivation of the governing eigenvalue equation the vibratory characteristics of annular sector plates with variations in boundary condition sector angle and thickness are examined the accuracy of the method is validated through appropriate convergence and comparison studies the first known results presented here provide a basis for understanding the physics of vibrations of annular sector plates and can be used to assess numerical results obtained from various refined two dimensional theories

eigenvalue spacings and dynamical upper bounds for discrete one dimensional schrodinger operators we prove dynamical upper bounds for discrete one dimensional schrodinger operators in terms of various spacing properties of the eigenvalues of finite volume approximations we demonstrate the applicability of our approach by a study of the fibonacci hamiltonian

the n soliton solutions of the sine gordon equation with self consistent sources abstract the hierarchy of the sine gordon equation with self consistent sources is derived by using the eigenfunctions of recursion operator the bilinear form of the sine gordon equation with self consistent sources is given and the n soliton solutions are obtained through hirota method and wronskian technique respectively some novel determinantal identities are presented to treat the nonlinear term in the time evolution and finish the wronskian verifications

solutions spectrum and dynamics for schrodinger operators on infinite domains 1 introduction and main results in this paper we investigate the relations between the rate of decay of solutions of schrodinger equations continuity properties of spectral measures of the corresponding operators and dynamical properties of the corresponding quantum systems the first main result of this paper shows that in great generality certain upper bounds on the rate of growth of l 2 norms of generalized eigenfunctions over expanding balls imply certain minimal singularity of the spectral measures consider an operator h v defined by the differential expression h v v x

on the use of orthogonal polynomials in the rayleigh ritz method for the study of the flexural vibration and buckling of isotropic and orthotropic rectangular plates series composed of recently proposed orthogonal polynomial functions are used in the rayleigh ritz method to generate results for a number of flexural vibration and buckling problems for rectangular isotropic and orthotropic plates it is demonstrated that the approach yields excellent results not only for natural frequencies and buckling loads but also for the more sensitive mode shape bending moment and shear force distribution problem

vibration of tapered thickness annular sector plates by spline element method abstract this paper deals with the determination of the vibrations of thin annular sector plates of tapered thickness by using the spline element method to demonstrate the accuracy of the present method several examples are solved and results are compared with those obtained by analytical methods and other numerical methods good accuracy is obtained frequencies of tapered annular sector plates with several boundary conditions are analyzed for the different sector angles and thickness parameters

non linear transient analysis of moderately thick laminated composite plates the non linear transient analysis of the shear deformable laminated composite plates subjected to step ramp and sinusoidal loading is presented the clamped simply supported free and their combinations non levy type of boundary conditions are considered the formulation is based on the mindlin first order shear deformation theory and von karman non linearity the methodology of the solution is based on the chebyshev series technique houbolt time marching scheme and quadratic extrapolation technique are used for the temporal discretization and linearization respectively the effects of magnitude and duration of loading rotary inertia in plane inertia b a a h lamination scheme and boundary conditions on the central displacement response are studied typical results are presented in dimensionless graphical forms for different parameters and loading conditions

generalized darboux transformations for the kp equation with self consistent sources the kp equation with self consistent sources kpescs is treated in the framework of the constrained kp equation this offers a natural way to obtain the lax representation for the kpescs based on the conjugate lax pairs we construct the generalized binary darboux transformation with arbitrary functions in time t for the kpescs which in contrast to the binary darboux transformation of the kp equation provides a non auto backlund transformation between two kpescss with different degrees the formula for n times repeated generalized binary darboux transformation is proposed and enables us to find the n soliton solution and lump solution as well as some other solutions of the kpescs

dynamical upper bounds on wavepacket spreading we derive a general upper bound on the spreading rate of wavepackets in the framework of schrodinger time evolution our result consists of showing that a portion of the wavepacket cannot escape outside a ball whose size grows dynamically in time where the rate of this growth is determined by properties of the spectral measure and by spatial properties of solutions of an associated time independent schrodinger equation we also derive a new lower bound on the spreading rate which is strongly connected with our upper bound we apply these new bounds to the fibonacci hamiltonian the most studied one dimensional model of quasicrystals as a result we obtain for this model upper and lower dynamical bounds establishing wavepacket spreading rates which are intermediate between ballistic transport and localization the bounds have the same qualitative behavior in the limit of large coupling

3 d vibration analysis of annular sector plates using the chebyshev ritz method abstract the three dimensional free vibration of annular sector plates with various boundary conditions is studied by means of the chebyshev ritz method the analysis is based on the three dimensional small strain linear elasticity theory the product of chebyshev polynomials satisfying the necessary boundary conditions is selected as admissible functions in such a way that the governing eigenvalue equation can be conveniently derived through an optimization process by the ritz method the boundary functions guarantee the satisfaction of the geometric boundary conditions of the plates and the chebyshev polynomials provide the robustness for numerical calculation the present study provides a full vibration spectrum for the thick annular sector plates which cannot be given by the two dimensional 2 d theories such as the mindlin theory comprehensive numerical results with high accuracy are systematically produced which can be used as benchmark to evaluate other numerical methods the effect of radius ratio thickness ratio and sector angle on natural frequencies of the plates with a sector angle from 120 to 360 is discussed in detail the three dimensional vibration solutions for plates with a re entrant sector angle larger than 180 and shallow helicoidal shells sector angle larger than 360 with a small helix angle are presented for the first time

quantum dynamics via complex analysis methods general upper bounds without time averaging and tight lower bounds for the strongly coupled fibonacci hamiltonian abstract we develop further the approach to upper and lower bounds in quantum dynamics via complex analysis methods which was introduced by us in a sequence of earlier papers here we derive upper bounds for non time averaged outside probabilities and moments of the position operator from lower bounds for transfer matrices at complex energies moreover for the time averaged transport exponents we present improved lower bounds in the special case of the fibonacci hamiltonian these bounds lead to an optimal description of the time averaged spreading rate of the fast part of the wavepacket in the large coupling limit this provides the first example which demonstrates that the time averaged spreading rates may exceed the upper box counting dimension of the spectrum

2d toda lattice equation with self consistent sources casoratian type solutions bilinear backlund transformation and lax pair the two dimensional toda lattice equation with self consistent sources is proposed based on its bilinear forms casoratian type solutions and backlund transformation bt for the bilinear forms are presented starting from the bt a lax pair is derived for the 2d toda lattice with self consistent sources

free vibration of annular sector plates with edges possessing different degrees of rotational restraint abstract results for the natural frequencies of annular sector plates possessing different degrees of elastic restraint along the edges are presented the analysis is based on a numerical method developed by the author the functions in the circumferential direction satisfying the boundary conditions along the radial edges which are required in the analysis are indicated to the best of the author s knowledge no previous results exist for such plates

in plane and shear buckling analysis of fg cntrc annular sector plates based on the third order shear deformation theory using a numerical approach abstract the buckling analysis of thick composite annular sector plates reinforced with functionally graded carbon nanotubes cnts is presented under in plane and shear loadings based on the higher order shear deformation theory it is considered that the plate is resting on the pasternak type elastic foundation the overall material properties of functionally graded carbon nanotube reinforced composites fg cntrcs are estimated through the micromechanical model the governing equations are derived on the basis of the higher order shear deformation plate theory and the quadratic form of the energy functional of the system is presented an efficient numerical method is presented in the context of variational formulation to obtain the discretized version of stability equations the validation of the present study is demonstrated through comparisons with the results available in the literature and then comprehensive numerical results are given to investigate the impacts of model parameters on the stability of cnt reinforced composite annular sector plates

fine structure of the zeros of orthogonal polynomials iv a priori bounds and clock behavior we prove locally uniform spacing for the zeros of orthogonal polynomials on the real line under weak conditions jacobi parameters approach the free ones and are of bounded variation we prove that for ergodic discrete schrodinger operators poisson behavior implies a positive lyapunov exponent both results depend on a priori bounds on eigenvalue spacings for which we provide several proofs

upper bounds in quantum dynamics of course the case of main interest is where h is given by l2 rd or 2 zd h is a schr dinger operator of the form a v and ip 0 is a localized wavepacket under the time evolution 1 the wavepacket i t will in general spread out with time finding quantitative bounds for this spreading in concrete cases and developing methods for proving such bounds has been the objective of a great number of papers in recent years one is often interested in the growth behavior of the moments of the position operator that is the function 11 x p 2 i 2 these questions are particularly complicated and interesting in situations where singular continuous spectra occur the discovery of the occurrence of such spectra for many models of physical relevance has triggered some activity on the quantum dynamical side for models with absolutely continuous spectra on the other hand quantum dynamical questions have been investigated much earlier in the context of scattering theory and have been answered to a great degree of satisfaction models with point spectrum or more restrictively models exhibiting anderson localization have also been investigated from a quantum dynamical point of view while it is not true in general that spectral localization implies dynamical localization 26 73 it has been shown that the three main approaches to spectral localization the fractional moment method 3 4 5 multi scale analysis 28 27 75 and the bourgain goldstein schlag method 12 37 yield dynamical localization as a by product 2 13 22 31 34 quantum dynamics for schr dinger operators with singular continuous spectra is much less understood the two primary examples motivated by physics are the harper model also known as the almost mathieu operator at critical cou pling which describes a bloch electron in a constant magnetic field with irrational flux through a unit cell and the fibonacci model which describes a standard one dimensional quasicrystal both models have been studied heavily in both the physics and mathematics communities

backlund transformations for the kp and mkp hierarchies with self consistent sources using gauge transformations for the corresponding generating pseudo differential operators ln in terms of eigenfunctions and adjoint eigenfunctions we construct several types of auto backlund transformations for the kp hierarchy with self consistent sources kphscs and mkp hierarchy with self consistent sources mkphscs respectively the backlund transformations from kphscs to mkphscs are also constructed in this way

vibration of rectangular plates with edge restraints and intermediate stiffeners vibrations of stiffened plates with elastically restrained edges are analyzed by the rayleigh ritz method the first lower four frequencies for restrained plates with up to six intermediate stiffeners are calculated the results of this study are compared with existing data and the agreement is excellent

dynamic response of various von karman non linear plate models and their 3 d counterparts dynamic von karman plate models consist of three coupled non linear time dependent partial differential equa tions these equations have been recently solved numerically kirby r yosibash z 2004 solution of von karman dynamic non linear plate equations using a pseudo spectral method comp meth appl mech eng 193 6 8 575 599 and yosibash z kirby r gottlieb d 2004 pseudo spectral methods for the solution of the von karman dynamic non linear plate system j comp phys 200 432 461 by the legendre collocation method in space and the implicit newmark b scheme in time where highly accurate approximations were realized due to their complexity these equations are often reduced by discarding some of the terms associated with time derivatives which are multiplied by the plate thickness squared being a small parameter because of the non linearities in the system of equations we herein quantitatively investigate the influence of these a priori assumption on the solution for different plate thicknesses as shown the dynamic solutions of the so called simplified von karman system do not differ much from the complete von karman system for thin plates but may have differences of few percent for plates with thicknesses to length ratio of about 1 20 nevertheless when investigating the modeling errors i e the difference between the various von karman models and the fully three dimensional non linear elastic plate solution one realizes that for relatively thin plates thickness is 1 20 of other typical dimensions this difference is much larger this implies that the simplified von karman plate model used frequently in the literature is as good as an approximation as the com plete and more complicated model as a side note it is shown that the dynamic response of any of the von karman plate models is completely different compared to the linearized plate model of kirchhoff love for deflections of an order of magnitude as the plate thickness 2004 elsevier ltd all rights reserved

on the analysis of laterally vibrating slender beams subject to various complicating effects the rayleigh ritz method with orthogonally generated polynomials as admissible functions is used to obtain a simple analysis of the free vibration problem of slender beams subject to various complicating effects these effects are the presence of concentrated masses and or concentrated moments of inertia intermediate supports axial loading and non uniformity of cross section such may exist separately or in any combination numerical results are presented for several example beams illustrating the accuracy and versatility of the approach

solution of von karman dynamic non linear plate equations using a pseudo spectral method abstract the von karman non linear dynamic partial differential system over rectangular domains is solved by the chebyshev collocation method in space and the implicit newmark time marching scheme in time in the newmark scheme a non linear fixed point iteration algorithm is employed we monitor both temporal and spatial discretization errors based on derived analytical solutions demonstrating highly accurate approximations we also quantify the influence of a common modeling assumption which neglects the in plane inertia terms in the full von karman system demonstrating that it is justified a comparison of our steady state von karman solutions to previous results in the literature and to a three dimensional high order finite element analysis is performed showing an excellent agreement other modeling assumptions such as neglecting in plane quadratic terms in the strain expressions are also addressed

chebyshev series solution to non linear boundary value problems in rectangular domain abstract the von karman equations governing the behavior of moderately large deformations of rectangular plates are expressed in displacement field a methodology based on chebyshev polynomials approximation to analyze the non linear boundary value problems in rectangular domain is developed these non linear partial differential equations of motion are linearized using quadratic extrapolation techniques the inertia and dissipative terms are evaluated by employing houbolt implicit time marching scheme the spatial discretization of the differential equations generates incompatibility viz greater number of equations than the unknowns the multiple linear regression analysis based on the least square error norm is employed to overcome the incompatibility and a compatible solution is obtained convergence study has been carried out the clamped and simply supported immovable rectangular plates subjected to static and dynamic loadings are analyzed results have been compared with the results obtained by other numerical and analytical methods

free and forced vibrations of plates by boundary and interior elements a direct boundary element method is developed for the dynamic analysis of thin elastic flexural plates of arbitrary planform and boundary conditions the formulation employs the static fundamental solution of the problem and this creates not only boundary integrals but surface integrals as well owing to the presence of the inertia force thus the discretization consists of boundary as well as interior elements quadratic isoparametric elements and quadratic isoparametric or constant elements are employed for the boundary and interior discretization respectively both free and forced vibrations are considered the free vibration problem is reduced to a matrix eigenvalue problem with matrix coefficients independent of frequency the forced vibration problem is solved with the aid of the laplace transform with respect to time and this requires a numerical inversion of the transformed solution to obtain the plate dynamic response to arbitrary transient loading the effect of external viscous or internal viscoelastic damping on the response is also studied the proposed method is compared against the direct boundary element method in conjunction with the dynamic fundamental solution as well as the finite element method primarily by means of a number of numerical examples these examples also serve to illustrate the use of the proposed method

the deduction of the lax representation for constrained flows from the adjoint representation for x and tn finite dimensional hamiltonian systems obtained from the decompositions of zero curvature equations it is shown that their lax representations can be deduced directly from the adjoint representations of the auxiliary linear problems as a consequence the zero curvature representation for soliton hierarchy with source is presented

spectral and dynamical properties of certain random jacobi matrices with growing parameters in this paper a family of random jacobi matrices with off diagonal terms that exhibit power law growth is studied since the growth of the randomness is slower than that of these terms it is possible to use methods applied in the study of schr odinger operators with random decaying potentials a particular result of the analysis is the existence of operators with arbitrarily fast transport whose spectral measure is zero dimensional the results are applied to the infinite dumitriu edelman model 2002 and its spectral properties are analyzed

natural vibration of circular and annular thin plates by hamiltonian approach abstract the present paper deals with the natural vibration of thin circular and annular plates using hamiltonian approach it is based on the conservation principle of mixed energy and is constructed in a new symplectic space a set of hamiltonian dual equations with derivatives with respect to the radial coordinate on one side of the equations and to the angular coordinate on the other side are obtained by using the variational principle of mixed energy the separation of variables is employed to solve hamiltonian dual equations of eigenvalue problem analytical frequency equations are obtained based on different cases of boundary conditions the natural frequencies are the roots of the frequency equations and corresponding mode functions are in terms of the dual variables q1 r three basic edge constraint cases for circular plates and nine edge constraint cases for annular plates are calculated and the results are compared well with existing ones

power law bounds on transfer matrices and quantum dynamics in one dimension we present an approach to quantum dynamical lower bounds for discrete one dimensional schrodinger operators which is based on power law bounds on transfer matrices it suffices to have such bounds for a nonempty set of energies we apply this result to various models including the fibonacci hamiltonian

on the free transverse vibration of annular and circular thin sectorial plates subject to certain complicating effects abstract the rayleigh ritz method with orthogonally generated polynomials as admissible functions is used to obtain an eigenvalue equation for the free transverse vibration of thin annular sectorial plates circular sectorial plates are treated with this equation by permitting the inner radius to become negligibly small the plates may be of isotropic or polar orthotropic material of uniform or radially and or circumferentially varying thickness and may include interior circumferential or radial line supports numerical values for the natural frequency parameters of several different plates are presented and compared with previously published values where available

differential quadrature method for vibration analysis of shear deformable annular sector plates this paper presents differential quadrature solutions for free vibration analysis of moderately thick annular sector plates based on the mindlin first order shear deformation theory numerical characteristics of the differential quadrature method are illustrated through solving selected annular sector plates with different boundary conditions relative thickness ratios inner to outer radius ratios and various sector angles parametric studies in terms of the vibration frequency parameters are thoroughly investigated

integrability of the semi discrete toda equation with self consistent sources a new procedure to construct and solve soliton equations with self consistent sources sescss is applied to the semi discrete toda equation based on its bilinear from bilinear backlund transformation bt for the semi discrete toda escs is presented starting from the bt a lax pair is derived for the semi discrete toda escs

transverse vibrations of a rotating uniform cantilever beam with tip mass as predicted by using beam characteristic orthogonal polynomials in the rayleigh ritz method abstract natural frequencies and mode shapes of a rotating uniform cantilever beam with a tip mass are studied by using beam characteristic orthogonal polynomials in the rayleigh ritz method the set of orthogonal polynomials which satisfy the geometrical boundary conditions are generated by using the gram schmidt process the results are compared with those obtained by the myklestad method the extended galerkin method and finite element methods the variation of natural frequencies with the speed of rotation is plotted for several parameter combinations such as setting angle tip mass moment of inertia of tip mass etc mode shapes at different rotational speeds are also plotted use of orthogonal polynomials for the deflection shapes enables the computation of higher natural frequencies of any order to be accomplished without facing any numerical difficulties which is not the case when arbitrary polynomial expressions are used

on the lateral vibration of thin annular and circular composite plates subject to certain complicating effects abstract series comprising orthogonally generated polynomial functions are used in the rayleigh ritz method to obtain an eigenvalue equation for the flexural vibration of thin flat annular and circular plates the plates may be of isotropic or polar orthotropic material of uniform or radially varying thickness and may pass over intermediate concentric ring supports numerical results are presented for a number of plates illustrating the versatility and accuracy of the approach

stability and vibration of mindlin sector plates an analytical approach this study presents a simple analytical formulation for the eigenvalue problem of buckling and free vibration analysis of mindlin sector plates the nonaxisymmetric formulation in cylindrical coordinates is discretized in the space domain in terms of two dimensional chebyshev polynomials the formulation facilitates application of several combinations of simply supported clamped and free edge conditions convergence study has been carried out and the obtained results are compared with those available in the literature extensive results pertaining to critical buckling loads and natural frequencies are presented effects of boundary conditions plate thickness and annularity are studied

on the pfaffianized kp equation with self consistent sources abstract a new procedure called source generation is applied to the pfaffianized kp equation as a result the pfaffianized kp equation with self consistent sources escs is obtained this coupled system cannot only be reduced to the pfaffianized kp equation but also reduced to the kp equation with self consistent sources kpescs so the pfaffianized kp escs can be viewed as a pfaffian version of the kpescs which indicates the commutativity of the source generation procedure and pfaffianization

on the two dimensional leznov lattice equation with self consistent sources a two dimensional leznov lattice equation with self consistent sources leznovescs is presented through the source generation procedure starting from the casoratian determinant solution of the two dimensional leznov lattice equation as a result the casoratian determinant solution of the leznovescs is obtained besides we also give the grammian determinant solution of the coupled system in addition the bilinear backlund transformation bt for the leznovescs is given

on the non isospectral kadomtsev petviashvili equation with self consistent sources abstract a new procedure called source generation is applied to construct non isospectral soliton equations with self consistent sources as results the non isospectral kadomtsev petviashvili equation with self consistent sources kpescs and its gramm type determinant solutions are obtained furthermore the non isospectral pfaffianized kp equation with self consistent sources is constructed this coupled system can not only be reduced to the non isospectral pfaffianized kp equation but also reduced to the non isospectral kpescs

new factorization of the kaup newell hierarchy abstract the new factorizations of each equation in the kaup newell kn hierarchy into two commuting x and t n finite dimensional integrable hamiltonian systems fdihs via the higher order potential eigenfunction constraints are presented the integrability commutativity and lax representation for these fdihss are deduced from the adjoint representations of the auxiliary linear problems for the kn hierarchy this approach provides a natural way to study soliton hierarchies with source the zero curvature representation and darboux transformation for the kn hierarchy with source related to eigenfunctions are found

the flexural vibration of rectangular plates with point supports abstract orthogonally generated polynomial functions are used in the lagrangian multiplier method to study the free flexural vibration problem of point supported thin flat rectangular plates the analysis applies to isotropic and specially orthotropic plates having any combination of clamped simply supported or free edges with arbitrarily located point supports and to plates which are continuous over line supports parallel to the plate edges numerical results are presented for a number of specific problems illustrating the accuracy and versatility of the approach and which include natural frequencies and nodal patterns for a point supported plate which is continuous over two perpendicular line supports

free vibration of annular sector plates by an integral equation technique abstract a numerical method is presented for the free vibration analysis of polar orthotropic clamped annular sector plates the results are compared with analytical and experimental values of other investigators a parametric study has been done by varying the sector angle and radii ratio the frequencies for isotropic and orthotropic cases are presented in the form of graphs

integration of the modified korteweg de vries hierarchy with an integral type of source the modified korteweg de vries hierarchy with an integral type of source mkdvhws which consists of the reduced akns eigenvalue problem with r q and the mkdv hierarchy with an extra term of the integration of a square eigenfunction is investigated we propose a method to find the explicit evolution equation for the eigenfunction of the auxiliary linear problems of the mkdvhws then we determine the evolution equations of scattering data corresponding to the mkdvhws and solve the equation in the mkdvhws by inverse scattering transformation

almost periodic schrodinger operators iii the absolutely continuous spectrum in one dimension we studyh d2 dx2 v x withv x limit periodic e g v x ancos x 2n with an we prove that for a genericv and for generican in the explicit example h is a cantor nowhere dense perfect set for a dense set the spectrum is both cantor and purely absolutely continuous and therefore purely recurrent absolutely continuous

absolutely continuous convolutions of singular measures and an application to the square fibonacci hamiltonian author s damanik d gorodetski a solomyak b abstract 2015 we prove for the square fibonacci hamiltonian that the density of states measure is absolutely continuous for almost all pairs of small coupling constants this is obtained from a new result we establish about the absolute continuity of convolutions of measures arising in hyperbolic dynamics with exact dimensional measures

solution of an initial boundary value problem for coupled nonlinear waves the authors derive and study a hierarchy of nonlinear coupled evolution equations among which is the coupled korteveg de vries schrodinger equation for which they prove that a mixed initial boundary value problem is solvable they give the method of solution together with the backlund transformation and establish the infinite set of conserved densities they finally discuss the applicability of such equations in plasma physics and hydrodynamics

fractal dimensions and the phenomenon of intermittency in quantum dynamics we exhibit an intermittency phenomenon in quantum dynamics more precisely we derive new lower bounds for the moments of order p associated to the state t e it h and averaged in time between zero and t these lower bounds are expressed in terms of generalized fractal dimensions d 1 1 p d of the measure where d is the space dimension this improves previous results obtained in terms of hausdorff and packing dimension

dynamical upper bounds for one dimensional quasicrystals abstract following the killip kiselev last method we prove quantum dynamical upper bounds for discrete one dimensional schrodinger operators with sturmian potentials these bounds hold for sufficiently large coupling almost every rotation number and every phase