the infinite horizon periodic review problem with setup costs and capacity constraints a partial characterization of the optimal policy the one item periodic review production and inventory system has been extensively studied in literature theories have been established for various basic constructs of the system of either finite or infinite horizon except for the case where production capacity is finite and production cost contains a fixed as well as a variable component it was conjectured in earlier research papers that the modified s s policy would be optimal to the finite capacity fixed cost model in infinite horizon this paper studies the long run limiting behavior of such systems it proves that the limiting cost function exists and there exist stationary policies that are optimal in the long run the optimal policy however is not of the modified s s type in general but continues to exhibit thex y band structure whenever the inventory level drops belowx order up to capacity when the inventory level is abovey do nothing when the inventory level is betweenx andy however the ordering pattern seems to be changing from problem to problem nevertheless based on a concept called c k convexity introduced in this paper thex y band is shown to be no more than one capacity of width one calculation for the bounds on suchx andy boundaries that are tight in some cases is also provided by exploring thex y band structure a linear program model is proposed to find the optimal policy completely finally an attempt is made to compare the best modified s s policy with the optimal one and a numerical example indicates that the deviation may be more than 11 in cost performance

the whitham hierarchies reductions and hodograph solutions a general scheme for analysing reductions of whitham hierarchies is presented it is based on a method for determining the s function by means of a system of first order partial differential equations compatibility systems of differential equations characterizing both reductions and hodograph solutions of whitham hierarchies are obtained the method is illustrated by exhibiting solutions of integrable models such as the dispersionless toda equation heavenly equation and the generalized benney system

second order pdes in four dimensions with half flat conformal structure we study second order partial differential equations pdes in four dimensions for which the conformal structure defined by the characteristic variety of the equation is half flat self dual or ant

an inventory model with limited production capacity and uncertain demands ii the discounted cost criterion this paper considers a single item periodic review inventory model with uncertain demands we assume a finite production capacity in each period with stationary data a convex one period cost function and a continuous demand distribution we show under a few additional unrestrictive assumptions that a modified basic stock policy is optimal under the discounted cost criterion both for finite and infinite planning horizons in addition we characterize the optimal base stock levels in several ways

lower dimensional reductions of gl m c self dual yang mills equation solutions with break of wave profiles any matrix self dual type s integrable partial differential equation pde possesses a family of lower dimensional reductions represented by the matrix quasilinear first order pdes solvable by the method of characteristics these pdes admit two types of particular solutions a explicit solutions and b implicit solutions represented by a system of nondifferential equations the latter solutions exhibit the break of wave profile 2 1 and 3 1 dimensional gl m c self dual yang mills equations have been considered as examples

linearly degenerate hierarchies of quasiclassical sdym type we demonstrate that sdym self dual yang mills equations for the lie algebra of one dimensional vector fields represent a natural reduction in the framework of a general linearly degenerate dispersionless hierarchy we define the reduction in terms of wave functions and introduce a generating relation lax sato equations and the dressing scheme for the reduced hierarchy a multidimensional case is also discussed

on a class of three dimensional integrable lagrangians we characterize non degenerate lagrangians of the form such that the corresponding euler lagrange equations are integrable by the method of hydrodynamic reductions the integrability conditions constitute an over determined system of fourth order pdes for the lagrangian density f which is in involution and possesses interesting differential geometric properties the moduli space of integrable lagrangians factorized by the action of a natural equivalence group is three dimensional familiar examples include the dispersionless kadomtsev petviashvili dkp and the boyer finley lagrangians f u x 3 3 u y 2 u x u t and respectively a complete description of integrable cubic and quartic lagrangians is obtained up to the equivalence transformations the list of integrable cubic lagrangians reduces to three examples there exists a unique integrable quartic lagrangian we conjecture that these examples exhaust the list of integrable polynomial lagrangians which are essentially three dimensional it was verified that there exist no polynomial integrable lagrangians of degree five we prove that the euler lagrange equations are integrable by the method of hydrodynamic reductions if and only if they possess a scalar pseudopotential playing the role of a dispersionless lax pair

reductions and hodograph solutions of the dispersionless kp hierarchy a general scheme for analysing reductions of dispersionless integrable hierarchies is presented it is based on a method for determining the s function by means of a system of first order differential equations compatibility systems of nonlinear partial differential equations of bourlet type characterizing both reductions and hodograph solutions of the dkp hierarchy are obtained wide classes of illustrative explicit examples are exhibited

lowast sdym fields and heavenly spaces i lowast sdym equations as an integrable system it is shown that the self dual yang mills sdym equations for the bracket lie algebra on a heavenly space can be reduced to one equation the master equation two hierarchies of conservation laws for this equation are constructed then the twistor transform and a solution to the riemann hilbert problem are given

on the integrability of 2 1 dimensional quasilinear systems a 2 1 dimensional quasilinear system is said to be integrable if it can be decoupled in infinitely many ways into a pair of compatible n component one dimensional systems in riemann invariants exact solutions described by these reductions known as nonlinear interactions of planar simple waves can be viewed as natural dispersionless analogues of n gap solutions it is demonstrated that the requirement of the existence of sufficiently many n component reductions provides the effective classification criterion as an example of this approach we classify integrable 2 1 dimensional systems of conservation laws possessing a convex quadratic entropy

the neatest many body problem amenable to exact treatments a goldfish various formulations findings and conjectures are reviewed which relate to a many body problem that is arguably the neatest nontrivial such model amenable to exact treatments

the moyal bracket and the dispersionless limit of the kp hierarchy a new lax equation is introduced for the kp hierarchy which avoids the use of pseudo differential operators as used in the sate approach this lax equation is closer to that used in the study of the dispersionless kp hierarchy and is obtained by replacing the poisson bracket with the moyal bracket the dispersionless limit under which the moyal bracket collapses to the poisson bracket is particularly simple

a dual reciprocity boundary element solution method for the free vibration analysis of fluid coupled kirchhoff plates abstract a boundary element solution method is proposed for linear vibration analysis of fluid coupled thin plates the method is based on replacing the associated biharmonic operator with two successive harmonic operators leading to a coupled system of boundary integral equations with simpler properties the fundamental solution has an elementary form and complicated singularity removal techniques can be avoided the fluid flow due to the plate motion is taken as a potential field and its effect on the plate dynamics is incorporated into the analysis by invoking another boundary integral solution described over the fluid plate interface the body terms in the plate boundary integral equations are considered by the dual reciprocity boundary element formulation three different radial basis functions are employed as interpolation functions alone and augmented with polynomial and sine expansions to represent the body terms the performance of the method is investigated from several perspectives by adopting plates with different shapes and or boundary conditions excellent approximations are obtained in general the convergence behavior is consistent both dry and wet frequency parameters are predicted accurately and the mode shapes are captured even with rough models in some of the studied problems however deviated results are obtained for specific modes furthermore it is observed that the performance of the method depends on the implemented drm functions and combining radial basis functions with global expansions does not yield noticeable improvements

direct evaluation of hypersingular galerkin surface integrals a direct algorithm for evaluating hypersingular integrals arising in a three dimensional galerkin boundary integral analysis is presented the singular integrals are defined as limits to the boundary and by integrating two of the four dimensions analytically the coincident integral is shown to be divergent however the divergent terms can be explicitly calculated and shown to cancel with corresponding singularities in the adjacent edge integrals a single analytic integration is employed for the edge and vertex singular integrals this is sufficient to display the divergent term in the edge adjacent integral and to show that the vertex integral is finite by explicitly identifying the divergent quantities we can compute the hypersingular integral without recourse to stokes s theorem or the hadamard finite part the algorithms are developed in the context of a linear element approximation for the laplace equation but are expected to be generally applicable as an example the algorithms are applied to solve a thermal problem in an exponentially graded material

a class of integrable hamiltonian systems whose solutions are perhaps all completely periodic we show that the dynamical system characterized by the complex equations of motion qj i qj k 1 k jnqjqkf qj qk j 1 n with f x x x is hamiltonian and integrable and we conjecture that all its solutions qj t j 1 n are completely periodic with a period that is a finite integral multiple of t 2 here n is an arbitrary positive integer is an arbitrary nonvanishing real constant y y is the weierstrass function with arbitrary semiperiods and are two arbitrary constants special cases are f x 2 coth x 1 r2 sinh2 x f x 2 coth x f x 2 sinh x f x 2 x 1 2x2 and of course f x 2 x these findings as well as the conjecture which is shown to be true in some of these special cases are based on the possibility to recast these equations of motion in the modified lax form l i l l m with l and m appropriate n n matrix functions of the n dynamical variables qj and of their time derivatives qj

differential geometric approach to the integrability of hydrodynamic chains the haantjes tensor the integrability of an m component system of hydrodynamic type u t v u u x by the generalized hodograph method requires the diagonalizability of the m m matrix v u this condition is known to be equivalent to the vanishing of the corresponding haantjes tensor we generalize this approach to hydrodynamic chains infinite component systems of hydrodynamic type for which the matrix v u is sufficiently sparse for such systems the haantjes tensor is well defined and the calculation of its components involves finite summations only we illustrate our approach by classifying broad classes of conservative and hamiltonian hydrodynamic chains with the zero haantjes tensor we prove that the vanishing of the haantjes tensor is a necessary condition for a hydrodynamic chain to possess an infinity of semi hamiltonian hydrodynamic reductions thus providing an easy to verify necessary condition for the integrability

solutions of a 2 1 dimensional dispersive long wave equation a special type of multisoliton solution with a particular dispersion relation is obtained for wu zhang equation which describes 2 1 dimensional dispersive long waves by the standard weiss tabor carnvale painleve truncation expansion using a nonstandard truncation of a modified conte s invariant painleve expansion two different types of soliton solutions without any dispersive relation is found two types of periodic wave solutions expressed by jacobi elliptic functions are found by the truncations of a special extended painleve expansion the soliton solutions are special cases of the corresponding periodic solutions

classification of integrable equations on quad graphs the consistency approach a classification of discrete integrable systems on quad graphs i e on surface cell decompositions with quadrilateral faces is given the notion of integrability laid in the basis of the classification is the three dimensional consistency this property yields among other features the existence of the discrete zero curvature representation with a spectral parameter for all integrable systems of the obtained exhaustive list the so called three leg forms are found this establishes lagrangian and symplectic structures for these systems and the connection to discrete systems of the toda type on arbitrary graphs generalizations of these ideas to the three dimensional integrable systems and to the quantum context are also discussed

three dimensional reductions of four dimensional quasilinear systems in this paper we show that four dimensional quasilinear systems of first order integrable by the method of two dimensional hydrodynamic reductions possess infinitely many three dimensional hydrodynamic reductions which are also integrable systems these three dimensional multi component integrable systems are irreducible to two dimensional hydrodynamic reductions in a generic case

dispersionless limit of the noncommutative potential kp hierarchy and solutions of the pseudodual chiral model in 2 1 dimensions the usual dispersionless limit of the kp hierarchy does not work in the case where the dependent variable has values in a noncommutative e g matrix algebra passing over to the potential kp hierarchy there is a corresponding scaling limit in the noncommutative case which turns out to be the hierarchy of a pseudodual chiral model in 2 1 dimensions pseudodual to a hierarchy extending ward s modified integrable chiral model applying the scaling procedure to a method generating exact solutions of a matrix potential kp hierarchy from solutions of a matrix linear heat hierarchy leads to a corresponding method that generates exact solutions of the matrix dispersionless potential kp hierarchy i e the pseudodual chiral model hierarchy we use this result to construct classes of exact solutions of the su m pseudodual chiral model in 2 1 dimensions including various multiple lump configurations

on integrability in grassmann geometries integrable systems associated with fourfolds in gr 3 5 let gr d n be the grassmannian of d dimensional linear subspaces of an n dimensional vector space v n a submanifold x gr d n gives rise to a differential system x that governs d dimensional submanifolds of v n whose gaussian image is contained in x systems of the form x appear in numerous applications in continuum mechanics theory of integrable systems general relativity and differential geometry they include such wellknown examples as the dispersionless kadomtsev petviashvili equation the boyer finley equation plebansky s heavenly equations and so on in this paper we concentrate on the particularly interesting case of this construction where x is a fourfold in gr 3 5 our main goal is to investigate differential geometric and integrability aspects of the corresponding systems x we demonstrate the equivalence of several approaches to dispersionless integrability such as the method of hydrodynamic reductions the method of dispersionless lax pairs integrability on solutions based on the requirement that the characteristic variety of system x defines an einstein weyl geometry on every solution integrability on equation meaning integrability in twistor theoretic sense of the canonical gl 2 r structure induced on a fourfold x gr 3 5 all these seemingly different approaches lead to one and the same class of integrable systems x we prove that the moduli space of such systems is 6 dimensional we give a complete description of linearisable systems the corresponding fourfold x is a linear section of gr 3 5 and linearly degenerate systems the corresponding fourfold x is the image of a quadratic map p4 99k gr 3 5 the fourfolds corresponding to generic integrable systems are not algebraic and can be parametrised by generalised hypergeometric functions

the approach to the dispersionless kp hierarchy the dispersionless limit of the scalar nonlocal problem is derived it is given by a special class of nonlinear first order equations a quasiclassical version of the dressing method is presented it is shown that the algebraic formulation of dispersionless hierarchies can be expressed in terms of properties of beltrami type equations the universal whitham hierarchy and in particular the dispersionless kp hierarchy turn out to be rings of symmetries for the quasiclassical problem pacs number 02 30 uk

on optimal policies for production inventory systems with compound poisson demand and setup costs in this paper we consider a single item one machine production inventory system with compound poisson demand the production facility may be on or off while on the production rate is constant and while off the production rate is zero system costs consist of switching costs and inventory and backlogging costs we provide conditions when s s policies are optimal under the long run average expected cost criterion these conditions are met in particular but not necessarily when the inventory costs are convex the developed method in the proof is easy to apply to more general cases moreover the method allows us to compute optimal policies very efficiently

the direct boundary element method in plate bending the direct boundary element method based on the rayleigh green identity is employed for the static analysis of kirchhoff plates the starting point is a slightly modified version of stern s equations the focus is on the implementation of the method for linear elements and a hermitian interpolation for the deflection w the concept of element matrices is developed and the cauchy principal values of the singular integrals are given in detail the treatment of domain integrals the handling of internal supports the properties of the solution and the effect of singularities are discused numerical examples illustrate the various techniques in the appendix the influence functions for the second and third derivatives of the deflection w are given

x y band and modified s s policy this paper considers the stochastic single item periodic review inventory problem most importantly we assume a finite production capacity per period and a production cost function containing a fixed as well as a variable component with stationary data a convex expected holding and shortage cost function we show that generally the modified s s policy is not optimal to the finite horizon problems the optimal policy does however show a systematic pattern which we call the x y band structure this x y band policy is interpreted as follows whenever the inventory level drops below x order up to capacity when the inventory level is above y do nothing if the inventory level is between x and y however the ordering pattern is different from problem to problem although the x and y bounds may change from period to period we prove the existence of a pair of finite x and y values that can apply for all the periods i e bounds on individual bounds one calculation for such x and y bounds that are tight in some cases is also provided by exploring the x y band structure we can drastically reduce the computation effort for finding the optimal policies

a comparative analysis of painleve lax pair and similarity transformation methods in obtaining the integrability conditions of nonlinear schrodinger equations we derive the integrability conditions of nonautonomous nonlinear schrodinger equations using the lax pair and similarity transformation methods we present a comparative analysis of these integrability conditions with those of the painleve method we show that while the painleve integrability conditions restrict the dispersion nonlinearity and dissipation gain coefficients to be space independent and the external potential to be only a quadratic function of position the lax pair and the similarity transformation methods allow for space dependent coefficients and an external potential that is not restricted to the quadratic form the integrability conditions of the painleve method are retrieved as a special case of our general integrability conditions we also derive the integrability conditions of nonautonomous nonlinear schrodinger equations for two and three spacial dimensions

scalar second order evolution equations possessing an irreducible sl2 valued zero curvature representation we find all scalar second order evolution equations that possess an sl2 valued zero curvature representation irreducible to a proper subalgebra of sl2 none of these zero curvature representations depends on a parameter that could serve as the spectral parameter

taming hypersingular integrals using dimensional continuation we use the method of dimensional continuation to isolate singularities in integrals containing products of green s functions or their derivatives rules for the extraction of the finite part of so called hypersingular integrals are developed which should be useful in methods based on boundary integral techniques in science and engineering in applications to potential theory electromagnetic scattering and crack dynamics in continuum mechanics boundary integrals now can be readily evaluated using computational techniques without recourse to complex analysis or contour distortions since the hypersingularities occurring in intermediate steps of the computations can be isolated and ignored while taking the finite parts of the integrals into account in a consistent manner we have also identified new forms of the dirac ensuremath delta function in d dimensions which are useful and convenient in the calculations a summary of the integrable singular integrals is given in tabular form we extend the considerations to a wider class of green s functions and present a theorem with additional results arising from it that shows that hypersingular integrals associated with three dimensional potential problems can be reduced to one dimensional finite integrals rather than two dimensional integrals again leading to direct evaluations in such cases these calculations are compared with existing results to show the efficacy of the approach

evaluation of supersingular integrals second order boundary derivatives the boundary integral representation of second order derivatives of the primary function involves second order hypersingular and third order supersingular derivatives of the green s function by defining these highly singular integrals as a difference of boundary limits interior minus exterior the limiting values are shown to exist with a galerkin formulation coincident and edge adjacent supersingular integrals are separately divergent but the sum is finite while the individual hypersingular integrals are finite moreover the cancellation of the supersingular divergent terms only requires a continuous interpolation of the surface potential and there is no continuity requirement on the surface flux the algorithm is efficient the non singular integrals vanish and the singular integrals are computed entirely analytically and accurate values are obtained for smooth surfaces however it is shown that a continuous linear interpolation is not appropriate for evaluation at boundary corners

a galerkin symmetric and direct bie method for kirchhoff elastic plates formulation and implementation a variational boundary element formulation is proposed for the solution of the elastic kirchhoff plate bending problem the stationarity conditions of an augmented potential energy functional are first discussed after addressing the topic of the choice of the test functions a regularization process based on integrations by parts is developed which allows to express the formulation in terms of double integrals the inner being at most weakly singular and the outer regular standard integration procedures may then be applied for their numerical evaluation in the presence of both straight and curved boundaries the normal slope and the vertical displacement must be c0 and c1 continuous respectively numerical examples show through comparisons with analytical solutions that a high accuracy is achieved

sdym fields and heavenly spaces ii reductions of the sdym system reductions of the self dual yang mills sdym system for bracket lie algebra to the husain park hp heavenly equation and to sl n c sdym equation are given an example of a sequence of su n chiral fields n 2 tending for n to a curved heavenly space is found

the τ function of the universal whitham hierarchy matrix models and topological field theories the universal witham hierarchy is considered from the point of view of topological field theories the function for this hierarchy is defined it is proved that the algebraic orbits of whitham hierarchy can be identified with various topological matter models coupled with topological gravity

analytical integration of singular kernels in symmetric boundary element analysis of kirchhoff plates summary an analytical integration method for evaluating the singular integrals arising in the construction of symmetric boundary element models is proposed referring to the analysis of kirchhoff plates kernels involved in the symmetric boundary formulation of kirchhoff plates exhibit singularities up to o 1 r 4 the proposed technique temporarily deactivates the singularities by using a limit approach and carries out the integration on contiguous boundary elements in order to smooth the singularities of the kernels through sufficiently continuous shape functions the paper contains a brief presentation of the boundary integral formulation of the kirchhoff plate with the explicit expressions of the fundamental solutions involved and the derivation of the symmetric boundary element model a detailed description of the proposed integration technique is presented which discusses the main steps of the analytical procedure and provides the final results the technique is illustrated through the discussion of a series of relevant cases including high singularities and referring to both collinear and corner supports copyright q 2008 john wiley sons ltd

looped cotangent virasoro algebra and non linear integrable systems in dimension 2 1 we consider a lie algebra generalizing the virasoro algebra to the case of two space variables we study its coadjoint representation and calculate the corresponding euler equations in particular we obtain a bi hamiltonian system that leads to an integrable non linear partial differential equation this equation is an analogue of the kadomtsev petviashvili of type b equation

the staircase method integrals for periodic reductions of integrable lattice equations we show in full generality that the staircase method papageorgiou et al 1990 phys lett a 147 106 14 quispel et al 1991 physica a 173 243 66 provides integrals for mappings and correspondences obtained as traveling wave reductions of systems of integrable partial difference equations we apply the staircase method to a variety of equations including the korteweg de vries equation the five point bruschi calogero droghei equation the quotient difference qd algorithm and the boussinesq system we show that in all these cases if the staircase method provides r integrals for an n dimensional mapping with then one can introduce q 2r variables which reduce the dimension of the mapping from n to q these dimension reducing variables are obtained as joint invariants of k symmetries of the mappings our results support the idea that often the staircase method provides sufficiently many integrals for the periodic reductions of integrable lattice equations to be completely integrable we also study reductions on other quad graphs than the regular lattice and we prove linear growth of the multi valuedness of iterates of high dimensional correspondences obtained as reductions of the qd algorithm

deforming the lie algebra of vector fields on s 1 inside the poisson algebra on t s 1 we study deformations of the standard embedding of the lie algebra vect s1 of smooth vector fields on the circle into the lie algebra of functions on the cotangent bundle t s1 with respect to the poisson bracket we consider two analogous but different problems a formal deformations of the standard embedding of vect s1 into the lie algebra of functions on t s1 s1 which are laurent polynomials on fibers and b polynomial deformations of the vect s1 subalgebra inside the lie algebra of formal laurent series on t s1

dispersionless integrable systems in 3d and einstein weyl geometry for several classes of second order dispersionless pdes we show that the symbols of their formal linearizations define conformal structures which must be einstein weyl in 3d or self dual in 4d if and only if the pde is integrable by the method of hydrodynamic reductions this demonstrates that the integrability of these dispersionless pdes can be seen from the geometry of their formal linearizations

a simple construction of recursion operators for multidimensional dispersionless integrable systems abstract we present a simple novel construction of recursion operators for integrable multidimensional dispersionless systems that admit a lax pair whose operators are linear in the spectral parameter and do not involve the derivatives with respect to the latter new examples of recursion operators obtained using our technique include inter alia those for the general heavenly equation which describes a class of anti self dual solutions of the vacuum einstein equations and a six dimensional equation resulting from a system of ferapontov and khusnutdinova

integrability via geometry dispersionless differential equations in three and four dimensions we prove that the existence of a dispersionless lax pair with spectral parameter for a nondegenerate hyperbolic second order partial differential equation pde is equivalent to the canonical conformal structure defined by the symbol being einstein weyl on any solution in 3d and self dual on any solution in 4d the first main ingredient in the proof is a characteristic property for dispersionless lax pairs the second is the projective behaviour of the lax pair with respect to the spectral parameter both are established for nondegenerate determined systems of pdes of any order thus our main result applies more generally to any such pde system whose characteristic variety is a quadric hypersurface

a direct approach for boundary integral equations with high order singularities summary boundary integral equations with extremely singular i e more than hypersingular kernels would be useful in several elds of applied mechanics particularly when second and third order derivatives of the primary variable are required however their denition and numerical treatment pose several problems in this paper it is shown how to obtain these boundary integral equations with still unnamed singularities and moreover how to eciently and reliably compute all the singular integrals this is done by extending in full generality the so called direct approach only for deniteness the method is presented for the analysis of the deection of thin elastic plates numerical results concerning integrals with singularities up to order r 4 are presented to validate the proposed algorithm copyright 2000 john wiley sons ltd

the haantjes tensor and double waves for multi dimensional systems of hydrodynamic type a necessary condition for integrability an invariant differential geometric approach to the integrability of 2 1 dimensional systems of hydrodynamic type is developed we prove that the existence of special solutions known as double waves is equivalent to the diagonalizability of an arbitrary matrix of the two parameter familysince the diagonalizability can be effectively verified by calculating the haantjes tensor this provides a simple necessary condition for integrability

optimal control of a brownian production inventory system with average cost criterion in this paper we study a stochastic production inventory system with finite production capacity and random demand the cumulative production and demand are modeled by a two dimensional brownian motion process there is a setup cost for switching on the production and a convex holding and shortage cost and our objective is to find the optimal production inventory control that minimizes the average cost both lost sales and backlog cases are studied for the lost sales model we show that within a large class of policies the optimal production strategy is either to produce according to an s s policy or never turn on the machine at all thus it is optimal for the firm to not enter the business whereas for the backlog model we prove that the optimal production policy is always of the s s type our approach first develops a lower bound for the average cost among a large class of nonanticipating policies and then shows that the value function of the desired policy reaches the lower bound the results offer insights on the structure of the optimal control policies as well as the interplays between system parameters

direct evaluation of double singular integrals and new free terms in 2d symmetric galerkin bem in this paper a new general algorithm is developed for the direct evaluation of all singular double integrals arising in the 2d galerkin bem including those with hypersingular kernels a distinguishing feature of the proposed method is that double singular integrals are treated as a whole that is not as inner integrals followed by outer ones therefore when applied to the symmetric galerkin bem the proposed technique is strictly symmetry preserving moreover a careful analysis of the limiting process is performed which shows that some new free terms may arise

localized excitations in 2 1 dimensional systems by means of a special variable separation approach a common formula with some arbitrary functions has been obtained for some suitable physical quantities of various 2 1 dimensional models such as the davey stewartson ds model the nizhnik novikov veselov nnv system asymmetric nnv equation asymmetric ds equation dispersive long wave equation broer kaup kupershmidt system long wave short wave interaction model maccari system and a general n m component ablowitz kaup newell segur akns system selecting the arbitrary functions appropriately one may obtain abundant stable localized interesting excitations such as the multidromions lumps ring soliton solutions breathers instantons etc it is shown that some types of lower dimensional chaotic patterns such as the chaotic chaotic patterns periodic chaotic patterns chaotic line soliton patterns chaotic dromion patterns fractal lump patterns and fractal dromion patterns may be found in higher dimensional soliton systems the interactions between the traveling ring type soliton solutions are completely elastic the traveling ring solitons pass through each other and preserve their shapes velocities and phases some types of localized weak solutions peakons are also discussed especially the interactions between two peakons are not completely elastic after the interactions the traveling peakons also pass through each other and preserve their velocities and phases however they completely exchange their shapes

boundary element analysis of kirchhoff plates with direct evaluation of hypersingular integrals the typical boundary element method bem for fourth order problems like bending of thin elastic plates is based on two coupled boundary integral equations one strongly singular and the other hypersingular in this paper all singular integrals are evaluated directly extending a general method formerly proposed for second order problems actually the direct method for the evaluation of singular integrals is completely revised and presented in an alternative way all aspects are dealt with in detail and full generality including the evaluation of free term coe cients numerical tests and comparisons with other regularization techniques show that the direct evaluation of singular integrals is easy to implement and leads to very accurate results copyright 1999 john wiley sons ltd

lax pairs galore a formula that yields an apparently but only apparently nontrivial lax pair for any nonlinear evolution pde in 1 1 dimensions possessing a local conservation law is presented several examples are exhibited

hydrodynamic reductions of multidimensional dispersionless pdes the test for integrability a d 1 dimensional dispersionless pde is said to be integrable if its n component hydrodynamic reductions are locally parametrized by d 1 n arbitrary functions of one variable the most important examples include the four dimensional heavenly equation descriptive of self dual ricci flat metrics and its six dimensional generalization arising in the context of sdiff 2 self dual yang mills equations given a multidimensional pde which does not pass the integrability test the method of hydrodynamic reductions allows one to effectively reconstruct additional differential constraints which when added to the equation make it an integrable system in fewer dimensions as an example of this phenomenon we discuss the second commuting flow of the dispersionless kp hierarchy considered separately this is a four dimensional pde which does not pass the integrability test however the method of hydrodynamic reductions generates additional differential constraints which reconstruct the full 2 1 dimensional dis

the characterization of two component 2 1 dimensional integrable systems of hydrodynamic type we obtain the necessary and sufficient conditions for a two component 2 1 dimensional system of hydrodynamic type to possess infinitely many hydrodynamic reductions these conditions are in involution implying that the systems in question are locally parametrized by 15 arbitrary constants it is proved that all such systems possess three conservation laws of hydrodynamic type and therefore are symmetrizable in godunov s sense moreover all such systems are proved to possess a scalar pseudopotential which plays the role of the dispersionless lax pair we demonstrate that the class of two component systems possessing a scalar pseudopotential is in fact identical with the class of systems possessing infinitely many hydrodynamic reductions thus establishing the equivalence of the two possible definitions of integrability explicit linearly degenerate examples are constructed

on a class of integrable systems of monge ampere type we investigate a class of multi dimensional two component systems of monge ampere type that can be viewed as generalisations of heavenly type equations appearing in a self dual ricci flat geometry based on the jordan kronecker theory of the skew symmetric matrix pencils a classification of normal forms of such systems is obtained all two component systems of monge ampere type turn out to be integrable and can be represented as the commutativity conditions of parameter dependent vector fields geometrically systems of monge ampere type are associated with linear sections of the grassmannians this leads to an invariant differential geometric characterisation of the monge ampere property

integrable structure of the dirichlet boundary problem in multiply connected domains we study the integrable structure of the dirichlet boundary problem in two dimensions and extend the approach to the case of planar multiply connected domains the solution to the dirichlet boundary problem in the multiply connected case is given through a quasiclassical tau function which generalizes the tau function of the dispersionless toda hierarchy it is shown to obey an infinite hierarchy of hirota like equations which directly follow from properties of the dirichlet green function and from the fay identities the relation to multi support solutions of matrix models is briefly discussed

multidimensional integrable systems and deformations of lie algebra homomorphisms we use deformations of lie algebra homomorphisms to construct deformations of dispersionless integrable systems arising as symmetry reductions of anti self dual yang mills equations with a gauge group diff s1

on the central quadric ansatz integrable models and painleve reductions it was observed by tod 1995 class quantum grav 12 1535 47 and later by dunajski and tod 2002 phys lett a 303 253 64 that the boyer finley bf and the dispersionless kadomtsev petviashvili dkp equations possess solutions whose level surfaces are central quadrics in the space of independent variables the so called central quadric ansatz it was demonstrated that generic solutions of this type are described by painlev equations piii and pii respectively the aim of our paper is threefold 1 based on the method of hydrodynamic reductions we classify integrable models possessing the central quadric ansatz this leads to the five canonical forms including bf and dkp 2 applying the central quadric ansatz to each of the five canonical forms we obtain all painlev equations pi pvi with pvi corresponding to the generic case of our classification 3 we argue that solutions coming from the central quadric ansatz constitute a subclass of two phase solutions provided by the method of hydrodynamic reductions

integrable hydrodynamic chains a new approach for derivation of benney type moment chains and integrable hydrodynamic type systems is presented new integrable hydrodynamic chains are constructed all their hydrodynamical reductions are described and integrated new 2 1 integrable hydrodynamic type systems are found

from 2d integrable systems to self dual gravity we explain how to construct solutions to the self dual einstein vacuum equations from solutions of various two dimensional 2d integrable systems by exploiting the fact that the lax formulations of both systems can be embedded in that of the self dual yang mills equations we illustrate this by constructing explicit self dual vacuum metrics on where is a homogeneous space for a real subgroup of associated with the 2d system