matrix kadomtsev petviashvili equation matrix identities and explicit non singular solutions a new version of the backlund darboux transformation for the matrix kadomtsev petviashvili kp equation is used to construct and study explicit multi parameter solutions and wavefunctions in terms of the matrix exponents a class of the self adjoint non singular solutions of kp i is introduced using the controllability notion from the system theory a subclass of the rationally decaying self adjoint non singular solutions is studied in particular several results prove new in the scalar case also

a generalized depth estimation algorithm with a single image a depth estimation algorithm proposed by a p pentland 1987 is generalized in the proposed algorithm the raw image data in the vicinity of the edge is used to estimate the depth from defocus since no differentiation operation on the image data is required before the optimization process the method is less sensitive to the noise disturbance of measurements furthermore the edge orientation that was critical in pentland s approach will not be required in the case this algorithm is then applied to synthetic images containing various amounts of noise to test its performance experimental results indicate that the depth estimation errors are kept within 5 of true values on the average when it is applied to real images

einstein maxwell solitons the application of the inverse scattering method to the einstein maxwell equations for stationary axisymmetric exterior fields leads the authors to an explicit formula for the ernst and electromagnetic potentials of new exact solutions generated from an arbitrary seed solution

the asymptotic optimal frequency domain filter for edge detection in an earlier paper by shanmugam dickey and green an edge detection filter was derived which maximized the energy within a specified interval about an edge feature the initial expression of this filter involved a prolate spheroidal wave function however a careful analysis of the application of an asymptotic approximation to this function uncovered a major dimensional error the corrected derivation of the asymptotic optimal filter forms the subject of this paper to verify the results the filter found is compared to a similar filter developed independently by marr and hildreth

darboux transformations and exact solutions of two dimensional c 1 l and d 2 l 1 toda equations for the two dimensional toda equations corresponding to the kac moody algebras c 1 l and d 2 l 1 the darboux transformations which keep all the reductions of the lax pairs are constructed the lowest degrees of the darboux transformations are 2l 2 for c 1 l and 2l for d 2 l 1 exact solutions of these toda equations are presented in a purely algebraic way

a generalized formula for integrable classes of surfaces in lie algebras we discuss relations between the approach of fokas and gelfand to immersions on lie algebras and the theory of soliton surfaces of sym we show that many results concerning immersions on lie algebras can be reduced to or interpreted within the soliton surfaces approach we present also some new results including a generalization of the fokas gelfand formula for integrable classes of surfaces in lie algebras and in particular in pseudo euclidean n dim spaces the generalized formula is used to formulate a method of constructing integrable classes of surfaces as an example we discuss the class of linear weingarten surfaces defined by the linear relationship between gaussian and mean curvatures we construct explicitly a one parameter family of linear weingarten surfaces parallel equidistant to a given pseudospherical surface

pseudospherical surfaces on time scales a geometric definition and the spectral approach we define and discuss the notion of pseudospherical surfaces in asymptotic coordinates on time scales thus we extend well known notions of discrete pseudospherical surfaces and smooth pseudosperical surfaces on more exotic domains e g the cantor set in particular we present a new expression for the discrete gaussian curvature which turns out to be valid for asymptotic nets on any time scale we show that asymptotic chebyshev nets on an arbitrary time scale have constant negative gaussian curvature we present also the quaternion valued spectral problem the lax pair and the darboux backlund transformation for pseudospherical surfaces in asymptotic coordinates on arbitrary time scales

on the geometry of the inhomogeneous heisenberg ferromagnet nonintegrable case new classes of exact solutions of the inhomogeneous heisenberg ferromagnet equation are found by means of a geometrical technique this technique consists of calculating one parameter families of geodesics on surfaces in e3 the solutions correspond to geodesics on surfaces of rotation

darboux transformation and soliton like solutions for the gerdjikov ivanov equation an explicit n fold darboux transformation with multiparameters for a kind of coupled derivative nonlinear schrodinger equation is constructed with the help of a gauge transformation of a spectral problem as a reduction a darboux transformation of the gerdjikov ivanov equation is obtained furthermore the explicit soliton like solutions of the gerdjikov ivanov equation are given by applying its darboux transformation

on integrability of the inhomogeneous heisenberg ferromagnet model examination of a new test we present an improved version of the integrability test based on application of lie point transformations acting on the bare linear problem the test is then applied to the inhomogeneous heisenberg ferromagnet model equation the integrable cases selected by this test are identical with those obtained by the standard painleve test

darboux transformations finite reduction groups and related yang baxter maps in this paper we construct yang baxter yb maps using darboux matrices which are invariant under the action of finite reduction groups we present six dimensional yb maps corresponding to darboux transformations for the nonlinear schrodinger nls equation and the derivative nonlinear schrodinger dnls equation these yb maps can be restricted to four dimensional yb maps on invariant leaves the former are completely integrable and they also have applications to a recent theory of maps preserving functions with symmetries fordy a and kassotakis a 2013 j phys a math theor 46 205201 we give a six dimensional yb map corresponding to the darboux transformation for a deformation of the dnls equation we also consider vector generalizations of the yb maps corresponding to the nls and dnls equations

optimal edge detector design i parameter selection and noise effects this paper comments on the optimality of the laplacian of a gaussian edge detection filter which localizes edges through zero crossings in the filtered image the arguments of both marr and hildreth and dickey and shanmugam are reviewed to establish that the filter is optimal in the sense of maximizing output image energy near edge features this filter s principal advantage over other edge detectors is that its response is user adjustable through selection of a single parameter the gaussian standard deviation however no clear method for the selection of this parameter has been provided the problem is addressed here by applying the filter to two ideal periodic edge models blurred by a gaussian distribution point spread function the observed response to the edge spacing and blur standard deviation is then translated into a filter parameter design procedure the problems of optimum filter performance in the presence of additive gaussian noise are then addressed the problem of selecting the sampled filter s coefficient word size is dealt with in a companion paper

a new approach to the darboux backlund transformation versus the standard dressing method we present a new approach to the construction of the darboux matrix this is a generalization of a recently formulated method based on the assumption that the square of the darboux matrix vanishes for some values of the spectral parameter we consider the multisoliton case the reduction problem and the discrete case the relationships between our approach the zakharov shabat dressing method and the neugebauer meinel method are discussed in detail

quasideterminant solutions of the generalized heisenberg magnet model in this paper we present the darboux transformation for the generalized heisenberg magnet ghm model based on the general linear lie group gl n and construct multi soliton solutions in terms of quasideterminants further we relate the quasideterminant multi soliton solutions obtained by means of darboux transformation with those obtained by the dressing method we also discuss the model based on the lie group su n and obtain explicit soliton solutions of the model based on su 2

darboux covariant equations of von neumann type and their generalizations lax pairs with operator valued coefficients which are explicitly connected by means of an additional condition are considered this condition is proved to be covariant with respect to the darboux transformation of a general form nonlinear equations arising from the compatibility condition of the lax pairs in the matrix case include in particular nahm equations and volterra bogoyavlenskii and toda lattices the examples of other one two and multi field lattice equations are also presented

integrable evolution systems based on gerdjikov ivanov equations bi hamiltonian structure finite dimensional integrable systems and n fold darboux transformation a spectral problem and the associated gerdjikov ivanov gi hierarchy of nonlinear evolution equations is presented as a reduction the well known gi equation of derivative nonlinear schrodinger equations is obtained it is shown that the gi hierarchy is integrable in a liouville sense and possesses bi hamiltonian structure moreover the spectral problem can be nonlinearized as a finite dimensional completely integrable system under the bargmann constraint between the potentials and the eigenfunctions in particular an explicit n fold darboux transformation for the gi equation is constructed with the help of a gauge transformation of spectral problems and a reduction technique some explicit solitonlike solutions of the gi equation are given by applying its darboux transformation

darboux polynomial matrices the classical massive thirring model as a study case one way of constructing explicit expressions of solutions of integrable systems of partial differential equations goes via the darboux method this requires the construction of darboux matrices here we introduce a novel algorithm to obtain such matrices in polynomial form our method is illustrated by applying it to the classical massive thirring model and by combining it with the dihedral group of symmetries possessed by this model

an algebraic method to construct the darboux matrix we present an effective procedure to construct the 1 soliton darboux matrix our approach based on the zakharov shabat mikhailov s dressing method is especially useful in the case of non canonical normalization and for non isospectral linear problems the construction is divided into two steps first we represent a given linear problem as a system of some algebraic constraints on two matrices in this context we introduce and discuss invariants of the darboux matrix second we derive the darboux matrix demanding that it preserves the algebraic constraints in particular we consider in details the restrictions imposed by various reduction groups on the form of the darboux matrix

algebraic construction of the darboux matrix revisited we present algebraic construction of darboux matrices for 1 1 dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case we discuss different approaches to the darboux backlund transformation based on different dependences of the darboux matrix polynomial sum of partial fractions or the transfer matrix form we derive symmetric n soliton formulae in the general case the matrix spectral parameter and dressing actions in loop groups are also discussed we describe reductions to twisted loop groups unitary reductions the matrix lax pair for the kdv equation and reductions of chiral models harmonic maps to su n and to grassmann spaces we show that in the kdv case the nilpotent darboux matrix generates the binary darboux transformation the paper is intended as a review of known results usually presented in a novel context but some new results are included as well e g general compact formulae for n soliton surfaces and linear and bilinear constraints on the nonisospectral lax pair matrices which are preserved by darboux transformations

nonautonomous integrable nonlinear schrodinger equations with generalized external potentials inhomogeneous nonlinear schrodinger equations are constructed systematically using the covariance with respect to the darboux transformation the darboux invariants and the spectral parameter are functions of time and space which result in equations describing nonautonomous solitons moving in generalized external potentials all the known inhomogeneous nonlinear schrodinger equations as well as new ones of a more generalized form can be derived from the constructed equation one and two soliton solutions are explicitly constructed using the darboux transformation

wkb and spectral analysis of one dimensional schrodinger operators with slowly varying potentials consider a schrodinger operator on l 2 of the line or of a half line with appropriate boundary conditions if the potential tends to zero and is a finite sum of terms each of which has a derivative of some order in l 1 l p for some exponent p 2 then an essential support of the the absolutely continuous spectrum equals almost every generalized eigenfunction is bounded and satisfies certain wkb type asymptotics at infinity if moreover these derivatives belong to l p with respect to a weight x with 0 then the hausdorff dimension of the singular component of the spectral measure is strictly less than one

a discrete generalized coupled dispersionless integrable system and its multisoliton solutions abstract an integrable discretization of generalized coupled dispersionless dgcd integrable system via lax pair is presented a lax pair for the dgcd system is defined a darboux transformation is used on the lax pair to obtain multi soliton solutions of the dgcd system the solutions are expressed in terms of quasideterminants explicit expressions of discrete one and two soliton solutions are obtained for the s u 2 case by using properties of quasideterminants we also study continuous analogue of the dgcd system by applying continuum limit

a hierarchy of coupled korteweg de vries equations and the normalisation conditions of the hilbert riemann problem the authors discuss the normalisation conditions of the hilbert riemann problem which is of importance for the construction of the ladder of soliton solutions for a given spectral problem they provide the prescription for constructing the appropriate normalisation condition all this is applied to a new hierarchy of coupled korteweg de vries equations to find the soliton solution which displays some peculiar phenomena

the sine gordon equation on time scales abstract we formulate and discuss integrable analogue of the sine gordon equation on arbitrary time scales this unification contains the sine gordon equation discrete sine gordon equation and the hirota equation doubly discrete sine gordon equation as special cases we present the lax pair check compatibility conditions and construct the darboux backlund transformation finally we obtain a soliton solution on arbitrary time scale the solution is expressed by the so called cayley exponential function

an effective method to compute n fold darboux matrix and n soliton surfaces fairly simple formulas for an n fold darboux matrix and an n soliton addition to an arbitrary soliton surface embedded in e3 are proven they depend directly on the background wave function and are evidently symmetric with respect to n added solitons as an example an explicit expression for the interaction of n solitons on a single vortex filament is presented moreover there is given a simplified version of the n soliton formulas of neugebauer and meinel

the structure of spectral problems and geometry hyperbolic surfaces in e3 working in the framework of sym s soliton surfaces approach we point out that some simple assumptions about the structure of linear spectral problems of the theory of solitons lead uniquely to the geometry of some special immersions in this paper we consider general su 2 spectral problems under some very weak assumptions they turn out to be associated with hyperbolic surfaces surfaces of negative gaussian curvature immersed in three dimensional euclidean space and especially with the so called bianchi surfaces

bicomplexes and backlund transformations a bicomplex is a simple mathematical structure in particular associated with completely integrable models the conditions defining a bicomplex are a special form of a parameter dependent zero curvature condition we generalize the concept of a darboux matrix to bicomplexes and use it to derive backlund transformations for several models the method also works for moyal deformed equations with a corresponding deformed bicomplex

the darboux backlund transformation for the static 2 dimensional continuum heisenberg chain we construct the darboux backlund transformation for the sigma model describing static configurations of the 2 dimensional classical continuum heisenberg chain the transformation is characterized by a non trivial normalization matrix depending on the background solution in order to obtain the transformation we use a new more general spectral problem

multi soliton propagation in a generalized inhomogeneous nonlinear schrodinger maxwell bloch system with loss gain driven by an external potential in this paper we introduce a system of the nonlinear schrodinger maxwell bloch equation with variable coefficients which represents the propagation of optical pulses in an inhomogeneous erbium doped fiber with loss gain driven by an external potential the one and two soliton solutions in explicit forms are generated by using the darboux transformation and the associated lax pair we consider the distributed amplification system and some main features of the solutions are demonstrated graphically we also consider the concept of soliton propagation in a dispersion managed erbium doped fiber and through symbolic computation we have carried out our study from an analytic viewpoint

analysis of multichannel narrow band filters for image texture segmentation a model for texture analysis and segmentation using multiple oriented channel filters is analyzed in the general framework several different arguments are applied leading to the conclusion that the two dimensional gabor filters possess strong optimality properties for this task properties of the multiple channel segmentation approach are analyzed in particular perturbations of textures from an ideal model are found to have important effects on the segmentation that can usually be ameliorated by simply preceding the segmentation process by a logarithmic operation and using a low pass postfilter prior to making region assignments the difficult problems of space variant textures and multiple component textures are also considered local spatial frequency estimation approaches are suggested that use the responses as constraints in estimating the locally emergent texture frequencies complex texture aggregates containing multiple shared frequency components can be analyzed if the textures are distinct and few in number

darboux transformation of the generalized coupled dispersionless integrable system the darboux transformation on matrix solutions to the generalized coupled dispersionless integrable system based on a non abelian lie group is studied and the solutions are shown to be expressed in terms of quasideterminants as an explicit example the darboux transformation on scalar solutions to the system based on the lie group su 2 is discussed in detail and the solutions are shown to be expressed as ratios of determinants

a family of completely integrable multi hamiltonian systems explicitly related to some celebrated equations by introducing a spectral problem with an arbitrary parameter we derive a kaup newell type hierarchy of nonlinear evolution equations which is explicitly related to many important equations such as the kundu equation the kaup newell kn equation the chen lee liu cll equation the gerdjikov ivanov gi equation the burgers equation the modified korteweg devries mkdv equation and the sharma tasso olver equation it is shown that the hierarchy is integrable in liouville s sense and possesses multi hamiltonian structure under the bargann constraint between the potentials and the eigenfunctions the spectral problem is nonlinearized as a finite dimensional completely integrable hamiltonian system the involutive representation of the solutions for the kaup newell type hierarchy is also presented in addition an n fold darboux transformation of the kundu equation is constructed with the help of its lax pairs and a reduction technique according to the darboux transformation the solutions of the ku

on the localization performance measure and optimal edge detection the localization performance measure of edge detectors is addressed a one dimensional formulation of the problem is considered a linear space invariant filter is used for the detection the locations of local maxima in the thresholded output of the filter are declared to be the edges the limitations of conventional performance measures are shown and a localization performance measure for edge detection is suggested this performance measure is based on the theory of zero crossings of stochastic processes it is shown that the derivative of a gaussian is the optimal edge detector for the measure

darboux transformations and exact solutions of two dimensional a2n 2 toda equation the darboux transformations for two dimensional a2n 2 toda equation are constructed the lowest degree of the darboux transformation is 2 2n 1 if all the spectral parameters are complex or 2n 1 if one spectral parameter is real exact solutions are written down by computing the darboux transformations explicitly

quasideterminant solutions of an integrable chiral model in two dimensions the darboux transformation is used to obtain multisoliton solutions of the chiral model in two dimensions the matrix solutions of the principal chiral model and its lax pair are expressed in terms of quasideterminants the iteration of the darboux transformation gives the quasideterminant multisoliton solutions of the model it has been shown that the quasideterminant multisoliton solution of the chiral model is the same as obtained by zakharov and mikhailov using the dressing method based on the matrix riemann hilbert problem

geometrical and gauge equivalence of the generalized hirota heisenberg and wkis equations with linear inhomogeneities integrable evolution equations can take several equivalent forms in a geometrical sense here we consider the equivalence of generalized versions involving linear inhomogeneities of three important nonlinear evolution equations namely the hirota heisenberg ferromagnetic spin and wadati konno ichikawa shimizu wkis equation through a moving helical space curve formalism and stereographic representation from the geometrical consideration we also construct suitable 2 2 matrix linear eigenvalue equations involving however non isospectral flow the eigenvalues evolve in time however these systems are also gauge equivalent we briefly analyse the scattering problem and show that infinite number of constants of motion can exist for these systems