a recursive generation of local higher order sine gordon equations and their backlund transformation a new hierarchy of local nonlinear evolution equations is generated by a recursion operator and its explicit inverse it is shown that this hierarchy satisfies a canonical geometrical scheme and that it contains as special cases the sine gordon and liouville equations in laboratory coordinates a generalization of the well known backlund transformation and nonlinear superposition formula for the sine gordon equation is also obtained

the generalised zakharov shabat system and the gauge group action the generalized zakharov shabat systems with complex valued non regular cartan elements and the systems studied by caudrey beals and coifman cbc systems and their gauge equivalent are studied this study includes the properties of fundamental analytical solutions for the gauge equivalent to cbc systems and the minimal set of scattering data the description of the class of nonlinear evolutionary equations solvable by the inverse scattering method and the recursion operator related to such systems the hierarchies of hamiltonian structures the results are illustrated in the example of the multi component nonlinear schrodinger equations and the corresponding gauge equivalent multi component heisenberg ferromagnetic type models related to so 5 c algebra

factorization of operators ii we extend the methods of a previous paper j math phys 21 2508 1980 factorizing the general scalar third order differential operator and obtain a miura transformation for the boussinesq equation we give a general factorized eigenvalue problem we also give a hamiltonian structure associated with the factorized eigenvalue problem we derive several isospectral flows some of klein gordon type

polynomial lax pairs for the chiral o 3 field equations and the landau lifshitz equation new lax pairs for the chiral o 3 field equations and for the landau lifshitz equation have been found in contrast to the already known pairs these pairs are polynomial in the spectral parameter lambda we also find a new 4 4 lax pair in the case of cnoidal waves for the generalized landau lifshitz equation

hankel transform domain analysis of open circular microstrip radiating structures a full wave analysis of a circular disk conductor printed on a dielectric substrate backed by a ground plane is presented the method is based on the galerkin s method applied in the hankel transform domain and is numerically quite efficient several numerical examples are compared with available experimental data the agreement is found to be quite good and the validity of the present method is confirmed

an inverse problem for the dynamical lame system with two sets of boundary data we prove uniqueness and a holder type stability of reconstruction of all three time independent elastic parameters in the dynamical isotropic system of elasticity from two special sets of boundary measurements in proofs we use carleman type estimates in sobolev spaces of negative order 2003 wiley periodicals inc

two dimensional generalized toda lattice the zero curvature representation is obtained for the two dimensional generalized toda lattices connected with semisimple lie algebras the reduction group and conservation laws are found and the mass spectrum is calculated

completeness of the eigenfunctions for the caudrey beals coifman system the direct and the inverse scattering problem for the first order linear systems of the type l x i d dx q x j x 0 j h q x gj which generalizes the zakharov shabat system and the systems studied by caudrey beals and coifman cbc is analyzed herein here j is a regular complex constant element of the cartan subalgebra h g of the simple lie algebra g and the potential q x vanishes fast enough for x taking values in the image gj of adj the cbc results are generalized and the fundamental analytic solution m x for any choice of the irreducible finite dimensional representation v of g is constructed four pairwise equivalent minimal sets of scattering data for l invariant with respect to the choice of the representation of g are extracted from the asymptotics of m x for x from m x the resolvent of l is constructed in the adjoint representation vad and the completeness relation is proven for the eigenfunctions of l in vad it is also proven that the discrete spectrum

vector hankel transform analysis of annular ring microstrip antenna a rigorous analysis of the resonant frequency characteristics of an annular ring conductor printed on a dielectric substrate backed by a ground plane is presented the problem is cast into a set of vector dual integral equations by using vector hankel transform vht galerkin s method is then applied to compute the resonant frequencies of both transverse magnetic modes tm 11 and tm 12 of the microstrip antenna the real part of the resonant frequency shift of the tm 11 mode increases with increasing dielectric thickness in contrast to the tm 12 mode while the tm 11 mode has a high q it is a poor radiating mode the tm 12 mode is more suitable for antenna applications for a probe excitation the input impedance is obtained using single mode approximation for both the tm 11 and tm 12 modes it is shown that the tm 12 mode of the annular ring has a greater bandwidth than the tm 11 mode

nonlinear interaction of waves in elastodynamics and an inverse problem we consider nonlinear elastic wave equations generalizing gol dberg s five constants model we analyze the nonlinear interaction of two distorted plane waves and characterize the possible nonlinear responses using the boundary measurements of the nonlinear responses we solve the inverse problem of determining elastic parameters from the displacement to traction map

the squared eigenstates of the sine gordon eigenvalue problem an analysis of the squared sine gordon eigenvalue problem in laboratory coordinates is presented it is shown that unlike the unsquared laboratory coordinate eigenvalue problem the squared laboratory coordinate eigenvalue problem may be cast into the form of a standard eigenvalue problem wherein an eigenvalue independent operator operating on an eigenfunction generates the eigenvalue with this form it becomes rather elementary to obtain the squared eigenfunction expansion of the sine gordon potentials as well as to demonstrate closure

gauge covariant theory of the generating operator i a gauge covariant formulation of the generating operator operator theory for the zakharov shabat system is proposed the operator tilde lambda corresponding to the gauge equivalent system in the pole gauge is explicitly calculated thus the unified approach to the nonlinear schrodinger type equations based on is automatically reformulated with the help of tilde lambda for the heisenberg ferromagnet type equations consequently it is established that the conserved densities for the heisenberg ferromagnet type equations are polynomial ins x and itsx derivatives special attention is paid to the interrelation between the hierarchies of symplectic structures corresponding to the above mentioned families of gauge equivalent equations it is shown that the geometrical properties of the conjugated operator are gaugeindependent

a newly developed formulation suitable for matrix manipulation of layered medium green s functions based on a recently developed formulation of the dyadic green s function for layered media dglm this work gives the matrix element representation of the dglm for general rwg basis functions including basis functions straddling across different layers and half rwg basis function attached to an infinite ground plane it has been rigorously proved that this representation is absent of any undesired line integrals the same as the popular michalski zheng s formulation of type c this work also gives the analytical solution for some typical cylindrically symmetric problems which can be used to validate any formulation for layered medium problems

landau lifshitz and higher order nonlinear systems gauge generated from nonlinear schrodinger type equations new landau lifshitz ll and higher order nonlinear systems gauge generated from nonlinear schrodinger ns type equations are presented the consequences of gauge equivalence between different dynamical systems are discussed the gauge connections among various ll and ns equations are found and depicted through a schematic representation

method of analytical regularization in the analysis of axially symmetric excitation of imperfect circular disk antennas abstract this work presents accurate numerical method and computational results in the modeling of the axisymmetric radiation of resistive and thin dielectric circular disk on substrate antennas to simulate resistive and thin dielectric disk features we use two side generalized boundary conditions gbc the analysis is based on the singular integral equations ies and the method of analytical regularization mar exploiting a galerkin method gm with judicious basis functions which convert ies into the fredholm second kind infinite matrix equations unlike previously known numerical techniques this guarantees convergence and enables us to compute the solution with controlled accuracy even in sharp resonances numerical results demonstrate the effect of disk losses and transparency on the fundamental radiation phenomena and help improve antenna characteristics such as radiation efficiency

integrable equations and recursion operators related to the affine lie algebras ar 1 we have derived a family of equations related to the untwisted affine lie algebras ar 1 using a coxeter r 1 reduction they represent the third member of the hierarchy of soliton equations related to the algebra applying additional 2 involutions we also obtain the real hamiltonian forms of these equations we also give some particular examples and impose additional reductions

multilayered media green s functions in integral equation formulations a compact representation is given of the electric and magnetic type dyadic green s functions for plane stratified multilayered uniaxial media based on the transmission line network analog along the aids normal to the stratification furthermore mixed potential integral equations are derived within the framework of this transmission line formalism for arbitrarily shaped conducting or penetrable objects embedded in the multilayered medium the development emphasizes laterally unbounded environments but an extension to the case of a medium enclosed by a rectangular shield is also included

on the use of subsectional spline basis functions for efficient calculation of the rcs of a microstrip array of concentric annular rings over a wide frequency band the use of b splines in the radial direction is described for efficient calculation of the radar cross section rcs of a microstrip annular ring or array of concentric annular rings over a wide frequency band galerkin s method in the vector hankel transform vht domain is used to calculate the induced current density on the annular patches an algorithm is presented for a fast and accurate calculation of the scalar hankel transforms of b splines on an arbitrary nonuniform grid which plays an important role in the numerical calculation of the reaction integrals containing the scalar hankel transforms of b splines the accuracy and computational efficiency of the method and the convergence of the rcs results with respect to the number of segments along the radial direction are studied for some annular ring and concentric ring patches

reductions of n wave interactions related to low rank simple lie algebras i z2 reductions the analysis and the classification of all reductions for the nonlinear evolution equations solvable by the inverse scattering method is an interesting and still open problem we show how the second order reductions of the n wave interactions related to low rank simple lie algebras g can be embedded also in the weyl group of g this allows us to display along with the well known ones a number of new types of integrable n wave systems some of the reduced systems find applications to nonlinear optics

uniqueness of the density in an inverse problem for isotropic elastodynamics we consider the unique determination of the density of a nonhomogeneous isotropic elastic object from measurements made at the surface we model the behavior of the bounded 3 dimensional object by the linear hyperbolic system of operators for isotropic elastodynamics the material properties of the object its density and elastic properties correspond to the smooth coefficients of these differential operators the data for this inverse problem in the form of the correspondence between applied surface tractions and resulting surface displacements is modeled by the dynamic dirichlet to neumann map on a finite time interval in an earlier paper we show that the speeds c p s of compressional and sheer wave propagation through the object are uniquely determined by the dirichlet to neumann map here we extend that result by showing that the density is also determined in the interior by the dirichlet to neumann map in the case for example that c p 2c s at only isolated points in the object we use techniques from microlocal analysis and integral geometry to solve this fully three dimensional problem

derivative nonlinear schrodinger equations and hermitian symmetric spaces it is shown that to each hermitian symmetric space there corresponds an integrable system of generalised derivative nonlinear schrodinger equations nls the nonlinear terms are related to the curvature tensor of the associated symmetric space the hamiltonian form of the equations is presented the results are an extension of those presented in an earlier paper 1983 on generalised nls equations associated with symmetric and reductive homogeneous spaces

on the complete integrability of completely integrable systems the question of complete integrability of evolution equations associated ton n first order isospectral operators is investigated using the inverse scattering method it is shown that forn 2 e g for the three wave interaction additional nonlinear pointwise flows are necessary for the assertion of complete integrability their existence is demonstrated by constructing action angle variables this construction depends on the analysis of a natural 2 form and symplectic foliation for the groupsgl n andsu n

bi hamiltonian formulation of the o 3 chiral fields equations hierarchy via a polynomial bundle we investigate the hamiltonian structures of some hierarchy of evolution equations related to a polynomial bundle over the algebra sl 4 the bundle contains the polynomial lax pair for the o 3 chiral fields system and for that reason the corresponding hierarchy of nonlinear evolution equations is called the cf hierarchy it is known that the hamiltonian properties of the cf hierarchy may be explained as a consequence of the existence of compatible poisson structures arising from a different lie algebra structure defined over so 4 we show that the generating operator for the cf hierarchy can be regarded as a nijenhuis tensor on the manifold of potentials and then naturally this manifold is equipped with the poisson nijenhuis structure

on classification of soliton solutions of multicomponent nonlinear evolution equations we consider several ways of how one could classify the various types of soliton solutions related to multicomponent nonlinear evolution equations which are solvable by the inverse scattering method for the generalized zakharov shabat system related to a simple lie algebra g in doing so we make use of the fundamental analytic solutions the zakharov shabat dressing procedure the reduction technique and other tools characteristic for that method the multicomponent solitons are characterized by several important factors the subalgebras of g and the way these subalgebras are embedded in g the dimension of the corresponding eigensubspaces of the lax operator l as well as by additional constraints imposed by reductions

the generating operator for the n n linear system abstract the class of exactly integrable non linear evolution equations nlee related to the general first order n n linear problem is studied the set of independent scattering data j is determined and trace identities are obtained next we use a special integro differential operator and obtain the expansions of the potential and its variation in the eigenfunctions of these enable us to consider the inverse scattering method as a generalized fourier transform and to write down in a compact form the integrals of motion we prove that there exist a hierarchy of hamiltonian structures generated by at the end we calculate the symplectic form in terms of the scattering data variations

integral equation formulation of microstrip antennas the problem of a microstrip antenna covered by a dielectric is formulated in terms of coupled integro differential equations with the current distribution on the microstrip patch as an unknown variable galerkin s method is used to solve for the unknown patch current using the present formulation the resonant frequency and bandwidth of a rectangular microstrip antenna are determined and compared with experimental results

analytical expressions for spatial domain green s functions in layered media accurate and efficient formulas for computing spatial domain green s functions are presented in this paper to apply the formulas we only require a set of sample points of the spectral domain green s function sdgf on an integration path avoiding its singularities and an infinite domain tail path since the sampling is carried out for the integrand excluding the bessel function the number of sample points required is much smaller than the numerical integration method this aspect of the proposed method proves to be very advantageous for evaluating closed form green s functions at large source observer distances it is shown that the proposed formulas provide accurate results for both the near and far field regions as well as a wide range of material parameters such as lossless lossy left handed materials as well as multilayered substrates

full wave spectral analysis and design of annular patch antenna with electromagnetically coupled microstrip feed line this paper presents a full wave analysis and the ensuing design considerations of the annular patch antenna fed by an electromagnetically coupled microstrip line the numerical analysis employs the spectral domain version of the integral equation with the method of moments formulation the basis functions on the ring patch are the eigenmodes of the corresponding magnetic wall cavity and subsectional rooftop functions are employed on the access line both tm and te modes are used along with more efficient collective solenoidal modes mode sorting criteria are given to ensure uniform convergence efficient schemes are presented for the calculation of the spectral domain reaction integrals along with criteria to avoid calculation of negligible mode to mode couplings based on the spectral analysis of the matrix condition number very good agreement is shown with measured data and design considerations are given for matching the radiator

global uniqueness for an inverse boundary value problem arising in elasticity we prove that we can determine the lame parameters of an elastic isotropic inhomogeneous medium in dimensionsn 3 by making measurements of the displacements and corresponding stresses at the boundary of the medium

on the structure of nonlinear evolution equations integrable by the z2 graded quadratic bundle the general form of nonlinear evolution equations and their backlund transformations connected with the quadratic in the spectral parameter z2 graded arbitrary order linear matrix spectral problem is found the hamiltonian structure of the integrable equations is discussed the infinite family of poisson brackets which corresponds to the class of equations under consideration is given relativistic invariant integrable equations are considered the explicit forms of elementary and soliton backlund transformations are found a nonlinear superposition principle is obtained

an inverse problem in elastodynamics uniqueness of the wave speeds in the interior abstract we consider the unique determination of internal properties of a nonhomogeneous isotropic elastic object from measurements made at the surface the 3 dimensional object is modelled by solutions of the linear hyperbolic system of equations for elastodynamics whose leading coefficients correspond to the internal properties of the object its density and elasticity we model surface measurements by the dirichlet to neumann map on a finite time interval in a previous paper the author has shown that the density and elastic properties of the surface of the object are uniquely determined by the dirichlet to neumann map here we apply that result to conclude that certain properties of the interior of the object the wave speeds are also determined we then observe that the elastodynamic polarization is determined outside the object by the dirichlet to neumann map we conclude in the case that the wave speeds are constant that the polarization data do not determine the density in the interior this problem and techniques used in its study are closely related to those in for example seismology and medical imaging the techniques used here though from geometric optics integral geometry and microlocal analysis lead to the solution of this fully three dimensional problem

the soliton correlation matrix and the reduction problem for integrable systems integrable 1 1 dimensional systems associated to linear first order matrix equations meromorphic in a complex parameter as formulated by zakharov mikhailov and shabat 1 3 zms are analyzed by a new method based upon the soliton correlation matrix m matrix the multi backlund transformation which is equivalent to the introduction of an arbitrary number of poles in the zms dressing matrix is expressed by a pair of matrix riccati equations for them matrix through a geometrical interpretation based upon group actions on grassman manifolds the solution of this system is explicitly determined in terms of the solutions to the zms linear system reductions of the system corresponding to invariance under finite groups of automorphisms are also solved by reducing them matrix suitably so as to preserve the class of invariant solutions

hankel transform domain analysis of dual frequency stacked circular disk and annular ring microstrip antennas a theoretical and numerical analysis of the dual frequency stacked circular disk and annular ring microstrip antennas is discussed the problem is formulated in the hankel transform domain first the green s function is derived relating the transformed electric surface currents on the patches and the transformed tangential electric field components on the substrates galerkin s method is used with parseval s relation for hankel transformation to solve for the resonant frequencies and the unknown currents the far zone radiation patterns are expressed in terms of the transforms of the currents numerical results obtained for the resonant frequencies and radiation patterns are found to be in excellent agreement with the experimental data available in the literature

analysis of stacked microstrip patches with a mixed potential integral equation a method based on the mixed potential integral equation for the analysis of flat microstrip antennas in a double layer substrate is presented the method is used to compute the input impedance of a stacked patch configuration this structure permits a larger bandwidth and may also provide dual frequency operation the green s functions are discussed in detail and numerical results are obtained for the propagation constant of the dominant surface wave theoretical and experimental results are compared for a dual frequency and a broadband stacked patch antenna theoretical results for the input impedance are in good agreement with measurements the difference between theoretical and experimental results for the resonant frequency is less than 4 5 in all cases

input impedance of annular ring microstrip antennas with a dielectric cover a theoretical and numerical analysis of the annular ring microstrip antenna with a dielectric cover is performed the problem is formulated in the hankel transform domain taking a coaxial feed into consideration the integral equations for the surface current density on the patch are derived galerkin s method is used to solve for the surface current density and a stationary formula for the input impedance is obtained numerical results showing the effects of a dielectric cover on the tm sub 12 mode of the annular ring are given it is found that the dielectric cover reduces the resonant frequency decreases the resonant resistance and increases the impedance bandwidth

on the recursion operators for the gerdjikov mikhailov and valchev system we consider the recursion operator approach to the soliton equations related to an auxiliary linear system introduced recently by gerdjikov mikhailov and valchev gmv system we discuss the recursion operators obtained for the gmv system and show that they are particular cases of the generating operators related to a zakharov shabat type linear system on the algebra sl 3 c in pole gauge

propagation of polarization in elastodynamics with residual stress and travel times we show that knowing the displacement to traction map associated to the equations of isotropic elastodynamics with residual stress we can determine the lens maps of compressional and shear waves we derive several consequences of this for the inverse problem of determining the residual stress and the lame parameters from the displacement to traction map

resonance frequency of a rectangular microstrip patch the microstrip patch resonant frequency problem is formulated in terms of an integral equation using vector fourier transforms using galerkins s method in solving the integral equation the resonant frequency of the microstrip patch is studied with both chebyshev polynomials and sinusoidal functions as basis functions in the case of the chebyshev polynomials the edge singularity is included but it is not important for convergence furthermore the resonant frequency of the microstrip patch is ascertained with a perturbation calculation the results for galerkin s method and experiments are in good agreement the perturbation calculation agrees asymptotically with galerkin s method with the aim of developing a computer aided design formula the solutions obtained by galerkin s method are interpolated with a three variable polynomial

nonlinear schrodinger equations and simple lie algebras we associate a system of integrable generalised nonlinear schrodinger nls equations with each hermitian symmetric space these nls equations are considered as reductions of more general systems this time associated with a reductive homogeneous space the nonlinear terms are related to the curvature and torsion tensors of the appropriate geometrical space the hamiltonian structure is investigated using r matrix techniques and shown to be canonical for all these equations throughout the reduction procedure this hamiltonian structure does not degenerate each of the above systems of equations is gauge equivalent to a generalised ferromagnet reductions of the latter are discussed in terms of the corresponding nls type equations