on the interaction of nearly equal solitons in the kdv equation an asymptotic formula is derived that describes the interaction of two solitons travelling with nearly equal speeds as the sum of two solitons with time dependent parameters if the difference in s

physical optics analysis of multiple interactions in large scatters using current modes an efficient scheme based on physical optics po to analyze the mutual interactions between the parts of large bodies is presented the po current is approximated by current modes defined as complex exponential functions both the body geometry and the current modes are represented by means of nonuniform rational bi spline surfaces functions the current modes are computed by extrapolation considering the current values in a set of sampling points a new interpolation scheme to obtain the phase of the current modes using samples of the spatial frequency is presented the field due to the current modes is calculated efficiently using analytical expressions some results are also presented that show the performances of the method

on the optimal synthesis of sum or difference patterns of centrosymmetric arrays under arbitrary sidelobe constraints this paper deals with the optimal synthesis of sum or difference patterns radiated by an array of fixed geometry the aim is to establish the most general class of arrays for which such synthesis can be reduced to a linear programming problem extending and completing previous results regarding uniformly spaced linear and planar arrays it is shown that such a class consists of the centrosymmetric arrays whose element patterns are either equal or hermitian symmetric with respect to the center of symmetry the optimal solutions are also hermitian symmetric and the corresponding patterns are real furthermore it is shown that the above class of arrays coincides with that of the arrays capable of radiating real patterns some numerical examples are provided to give an idea of the geometries and the synthesis problems to which the achieved result successfully applies and of the achievable computational advantage

on the spatial bandwidth of scattered fields it is shown that the scattered fields are almost space bandlimited functions the effective bandwidth w is introduced and evaluated for a very general scattering system as well as the error made using functions bandlimited to w w for representing the scattered field the effective bandwidth is very simply related to the maximum dimension of the scattering system the error drops to negligible values for modest increases of w compared to w in the case of large scatterers important consequences of the above general results are finally stressed

strong converse for the classical capacity of optical quantum communication channels we establish the classical capacity of optical quantum channels as a sharp transition between two regimes one which is an error free regime for communication rates below the capacity and the other in which the probability of correctly decoding a classical message converges exponentially fast to zero if the communication rate exceeds the classical capacity this result is obtained by proving a strong converse theorem for the classical capacity of all phase insensitive bosonic gaussian channels a well established model of optical quantum communication channels such as lossy optical fibers amplifier and free space communication the theorem holds under a particular photon number occupation constraint which we describe in detail in this paper our result bolsters the understanding of the classical capacity of these channels and opens the path to applications such as proving the security of noisy quantum storage models of cryptography with optical links

optimal far field focusing of uniformly spaced arrays subject to arbitrary upper bounds in nontarget directions a new approach providing new theoretical results to the optimal far field focusing of uniformly spaced arrays subject to a completely arbitrary mask for sidelobe bounds is presented and discussed in both cases of linear or planar arrays with rectangular boundaries it is first shown that the problem can be formulated without any loss to performances on the maximum as a linear programming one guaranteeing a globally optimal solution second a sufficient uniqueness criterion for the solution of the overall problem is also developed which shows how the solution may not be unique as is actually the case when planar arrays are considered in addition further globally effective optimization procedures are proposed for the latter case in order to optimize directivity smoothness of excitations or other performance parameters in the set of equivalent solutions last an extension to planar arrays with a nonrectangular boundary is also given a thorough numerical analysis confirms the effectiveness of the approach proposed and of the solution codes developed

rapid solution of the wave equation in unbounded domains in this paper we propose and analyze a new fast method for the numerical solution of time domain boundary integral formulations of the wave equation we employ lubich s convolution quadrature method for the time discretization and a galerkin boundary element method for the spatial discretization the coefficient matrix of the arising system of linear equations is a triangular block toeplitz matrix possible choices for solving the linear system arising from the above discretization include the use of fast fourier transform fft techniques and the use of data sparse approximations by using fft techniques the computational complexity can be reduced substantially while the storage cost remains unchanged and is typically high using data sparse approximations the gain is reversed i e the computational cost is approximately unchanged while the storage cost is substantially reduced the method proposed in this paper combines the advantages of these two approaches first the discrete convolution related to the block toeplitz system is transformed into the discrete fourier image thereby arriving at a decoupled system of discretized helmholtz equations with complex wave numbers a fast data sparse e g fast multipole or panel clustering method can then be applied to the transformed system additionally significant savings can be achieved if the boundary data are smooth and time limited in this case the right hand sides of many of the helmholtz problems are almost zero and hence can be disregarded finally the proposed method is inherently parallel we analyze the stability and convergence of these methods thereby deriving the choice of parameters that preserves the convergence rates of the unperturbed convolution quadrature we also present numerical results which illustrate the predicted convergence behavior

fast analysis of transient electromagnetic scattering phenomena using the multilevel plane wave time domain algorithm the computational complexity of classical marching on in time mot methods for solving time domain integral equations tdies pertinent to the analysis of transient scattering phenomena involving perfectly conducting targets grows as o n sub t n sub s sup 2 n sub t and n sub s denote the number of temporal and spatial degrees of freedom dof of the electric current on the target this scaling law impedes the application of these schemes to the analysis of large scale scattering phenomena the recently developed plane wave time domain pwtd algorithm permits the rapid evaluation of transient wave fields generated by temporally bandlimited sources and hence the acceleration of marching on in time based tdie solvers previously we described a two level pwtd enhanced tdie solver for analyzing electromagnetic scattering from perfectly conducting targets the computational complexity of this algorithm scales as o n sub t n sub s sup 1 5 logn sub s here a multilevel pwtd scheme for rapidly evaluating electric fields due to temporally bandlimited electric current sources is described in addition a multilevel pwtd enhanced tdie solver for analyzing electromagnetic scattering from perfectly conducting scatterers using o n sub t n sub s log sup 2 n sub s cpu resources is outlined last the accuracy and cpu memory efficiency of this solver are demonstrated by analyzing transient scattering from electrically large bodies

exact sampling approach for reflector antennas analysis a new method for computing the far field of a possibly shaped or deformed reflector antenna based on a sampling representation of the radiation integral is presented using a projection technique the required samples can be efficiently computed using a two dimensional fast fourier transform fft whereas the radiated field is reconstructed via standard sampling expansion numerical examples and computation time analysis are reported showing the effectiveness of the approach particularly for deformed reflectors and or plane cut field evaluation

a multilevel cartesian non uniform grid time domain algorithm a multilevel cartesian non uniform grid time domain algorithm cngtda is introduced to rapidly compute transient wave fields radiated by time dependent three dimensional source constellations cngtda leverages the observation that transient wave fields generated by temporally bandlimited and spatially confined source constellations can be recovered via interpolation from appropriately delay and amplitude compensated field samples this property is used in conjunction with a multilevel scheme in which the computational domain is hierarchically decomposed into subdomains with sparse non uniform grids used to obtain the fields for both surface and volumetric source distributions the computational cost of cngtda to compute the transient field at n s observation locations from n s collocated sources for n t discrete time instances scales as o n tn slogn s and o n tn slog 2n s in the low and high frequency regimes respectively coupled with marching on in time mot time domain integral equations cngtda can facilitate efficient analysis of large scale time domain electromagnetic and acoustic problems

soliton interactions for the korteweg devries equation a new perspective it can be shown that the n soliton solution of the korteweg devries equation can be decomposed into n separate solitons cf gardner et al 1974 calogero and degasperis and yoneyama 1982 however it is not immediately clear from the form of their solutions how the separate solitons relate directly to the single soliton solution here the two soliton case is considered and a decomposition is sought which can be clearly related to the single soliton solution although it appears that there is a family of such decompositions it is shown that only one of these is correct although this decomposition is equivalent to the decomposition given previously by gardner et al calogero and degasperis and yoneyama the form given here is different it is suggested that the form of solution produced here is a more appropriate representation of the solution since it is clear how it relates directly to the single soliton solution and it is easy through this form to analyse the interaction of the two solutions

majorization theory approach to the gaussian channel minimum entropy conjecture a long standing open problem in quantum information theory is to find the classical capacity of an optical communication link modeled as a gaussian bosonic channel it has been conjectured that this capacity is achieved by a random coding of coherent states using an isotropic gaussian distribution in phase space we show that proving a gaussian minimum entropy conjecture for a quantum limited amplifier is actually sufficient to confirm this capacity conjecture and we provide a strong argument towards this proof by exploiting a connection between quantum entanglement and majorization theory

gaussian optimizers for entropic inequalities in quantum information we survey the state of the art for the proof of the quantum gaussian optimizer conjectures of quantum information theory these fundamental conjectures state that quantum gaussian input states are the solution to several optimization problems involving quantum gaussian channels these problems are the quantum counterpart of three fundamental results of functional analysis and probability the entropy power inequality the sharp young s inequality for convolutions and the theorem gaussian kernels have only gaussian maximizers quantum gaussian channels play a key role in quantum communication theory they are the quantum counterpart of gaussian integral kernels and provide the mathematical model for the propagation of electromagnetic waves in the quantum regime the quantum gaussian optimizer conjectures are needed to determine the maximum communication rates over optical fibers and free space the restriction of the quantum limited gaussian attenuator to input states diagonal in the fock basis coincide

on the structure of the two soliton interaction for the korteweg de vries equation abstract in this paper we consider an interaction of two solitons represented by a two soliton solution of kdv unlike previous work on the subject we do not associate solitons with the maxima of the two soliton solution but with the poles of a certain singular solution which can be considered as a two antisoliton solution since it annihilates the original two soliton solution motion of these poles may be chosen to represent motion of the solitons participating in the interaction and unlike interaction of the two maxima interaction of the poles always proceeds in the same manner the faster one approaches the slower one at a minimal distance where they exchange identities and then separate

multisoliton solution of a class of coupled soliton equations abstract the n soliton solutions of the korteweg devries kdv and boussinesq equations with a source are obtained explicitly by using the bilinear transformation method also the interactions of two soliton solutions are studied and the explicit forms for the one and two soliton solutions are obtained for the two systems

a solution of gaussian optimizer conjecture for quantum channels the long standing conjectures of the optimality of gaussian inputs and additivity are solved for a broad class of gauge covariant or contravariant bosonic gaussian channels which includes in particular thermal additive classical noise and amplifier channels restricting to the class of states with finite second moments we show that the vacuum is the input state which minimizes the entropy at the output of such channels this allows us to show also that the classical capacity of these channels under the input energy constraint is additive and is achieved by gaussian encodings

on the role of the number of degrees of freedom of the field in mimo channels the aim of this paper is to investigate the relationship between the effective number of degrees of freedom endf of a multiple input multiple output mimo channel and the number of degrees of freedom ndf of the field in particular the ndf of the field represents an upperbound for the endf of a mimo channel consequently the evaluation of the maximum endf can be carried out by adopting the literature on the ndf based on the spatial bandlimitation properties of the field this approach allows a simple and intuitive explanation of the maximum endf in a mimo channel based on a geometrical interpretation of the spatial channel in terms of spatial nyquist intervals

the capacity of the quantum channel with general signal states it is shown that the capacity of a classical quantum channel with arbitrary possibly mixed states equals the maximum of the entropy bound with respect to all a priori distributions this completes the recent result of hausladen jozsa schumacher westmoreland and wootters 1996 who proved the equality for the pure state channel

an improved simple method for imaging the shape of complex targets the linear sampling method lsm is a simple and effective approach to image the shape of an unknown target through the solution of a linear equation whose known term is the field radiated by an elementary i e monopolar source located in a set of test points in this paper we extend the lsm formulation by generalizing the right hand side of the equation to higher order multipoles in particular we discuss which is the expected method s outcome after such a change and propose a post processing scheme to combine the results obtained for different multipoles as shown with simulated and experimental data the proper combination of higher order multipoles allows to achieve better images of complex shaped targets as compared to the standard lsm and to overcome some of its limitations

non propagating solitons of the non isospectral and variable coefficient modified kdv equation absbact the akns system associated with a non isospectral and variable coefficient mkdv equation is presented the method of inverse scattering is adapted to the non isospectral situation to determine the time evolution of the scattering data n soliton olutions are obtained examples of oscillating or standing one solitons with unusual dynamics are given an in depth study of the two soliton case is carried out by appropriately decomposing the solution into individual soliton elements in order to examine their interactions breathers are also constructed

error minimization of multipole expansion in this paper we focus on the truncation error of the multipole expansion for the fast multipole method and the multilevel fast multipole algorithm when the buffer size is large enough the error can be controlled and minimized by using the conventional selection rules on the other hand if the buffer size is small the conventional selection rules no longer hold and the new approach which we have recently proposed is needed however this method is still not sufficient to minimize the error for small buffer cases we clarify this fact and show that the information about the placement of true worst case interaction is needed a novel algorithm to minimize the truncation error is proposed

an effective near field far field transformation technique from truncated and inaccurate amplitude only data a general approach to the near field far field transformation from amplitude only near field data is presented the estimation of the far field is stated as an intersection finding problem and is solved by the minimization of a suitable functional the difficulties related to the possible trapping of the algorithm by a false solution common to any nonlinear inverse problem are mitigated by setting the problem in the space of the squared field amplitudes as already done in a number of existing papers and by incorporating all the a priori knowledge concerning the system under test in the formulation of the problem accordingly the a priori information concerning the far field the near field outside the measurement region and the accuracy of the measurement setup and its dynamic range are properly taken into account in the objective functional the intrinsic ill conditioning of the problem is managed by adopting a general flexible and nonredundant sampling representation of the field which takes into account the geometrical characteristics of the source as a consequence the number of unknowns is minimized and a technique is obtained which easily matches the available knowledge concerning the behavior of the field the effectiveness of the approach is shown by reporting the main results of an extensive numerical analysis as well as an experimental validation performed by using a very low cost near field facility available at the electronic engineering department university of napoli italy

note on the structure of a three solution of the korteweg devries equation in a recent publication the authors showed how to reformulate the n solition solution of the korteweg devries equation in such a way that the relationship between the n elements of the solution and the solitary wave solution of the equation is clearly apparent here this new formulation of the n soliton solution is used to analyse some of the properties during interaction of a three soliton solution of the equation

fast evaluation of the radiation patterns of true time delay arrays with beam steering a multilevel algorithm for the computation of the transient radiation patterns of true time delay ttd conformal arrays over a range of observation and beam steering directions is presented the multilevel algorithm is based on hierarchical decomposition of the array into smaller sub arrays of elements at the finest level of decomposition the angular temporal radiation patterns of single element sub arrays are obtained over a sparse angular grid of directions and short temporal duration by either measurement or calculation subsequent steps of the algorithm comprise multilevel aggregation of delayed sub array contributions this process continues until the transient radiation pattern of the whole array is obtained at each level the radiation pattern is interpolated to a finer angular grid of observations and steering directions followed by temporal delay compensation the multilevel array decomposition algorithm attains a computational complexity substantially lower than that of the direct evaluation furthermore the algorithm is particularly efficient for large arrays with large numbers of elements

singular value decomposition of the radiation operator application to model order and far field reduction the time harmonic electromagnetic scattering or radiation problem is considered the singular value decomposition svd is applied to the radiation operator that maps the set of electric and magnetic currents defined on the surface of an inhomogeneous object onto the set of the far fields scattered or radiated from this object the svd yields orthonormal bases for both sets because the radiation operator is compact and regularizing it is demonstrated that the far field calculated from the series expansions of the currents on these bases converges exponentially fast to the exact one if a sufficient number of terms is considered in these series this number is closely related to the degrees of freedom that characterize the far field the latter can be computed from a reduced number of unknowns in the discretized integral equation that links electric and magnetic surface currents by writing it in the new currents bases also it allows the reduction of the far field in a given angular sector the numerical complexity of this technique is addressed and 2d numerical examples are presented that illustrate its potentialities

a new method for avoiding the truncation error in near field antennas measurements a new method to avoid the truncation error in antenna near field measurements is presented the approach relies on the concept of information content of the field according to this point of view the truncation problem is solved by picking up the information that is lost due to the finite size of scanning area in points of the space reachable by the measurement system the method can be applied to any scanning geometry including the planar and cylindrical ones whenever the set up allows to vary the distance between the antenna under test and the probe during the scanning procedure application of the method to cylindrical near field scanning is numerically investigated assessing the effectiveness of the proposed technique

numerical accuracy of multipole expansion for 2d mlfma a numerical study of the multipole expansion for the multilevel fast multipole algorithm mlfma is presented in the numerical implementation of mlfma the error comes from three sources the truncation of the addition theorem the approximation of the integration the aggregation and disaggregation process these errors are due to the factorization of the green s function which is the mathematical core of the algorithm among the three error sources we focus on the truncation error and a new approach of selecting truncation numbers for the addition theorem is proposed using this approach the error prediction and control can be improved for the small buffer sizes and high accuracy requirements

on the structure during interaction of the two soliton solution of the korteweg de vries equation by analysing the structure during interaction of the soliton elements in the two soliton solution of the korteweg de vries equation it is shown how to calculate the duration of the interaction for two soliton elements with any amplitude ratio it is also clarified that the soliton elements as defined here always pass through one another irrespective of the magnitude of the amplitude ratio of the soliton elements this conclusion confirms most previous reports on the interaction of the soliton elements but contradicts another report which states that when amplitudes of the soliton elements are nearly equal the soliton elements do not pass through each other but rather advance toward each other bounce off one another and then recede from each other however it should be noted that in the last case the definition of the soliton elements is different from that given here

on the use of the singular value decomposition in the fast multipole method the authors present a new matrix compression algorithm to improve the efficiency of the fast multipole method fmm the method is based on the application of the singular value decomposition svd to the plane wave fmm aggregation matrices these matrices are low ranked which is exploited to provide alternative sets of orthonormal singular basis functions obtained as linear combinations of the original basis by choosing only the most relevant singular functions a much more compact representation is obtained to accurately handle the interactions between the fmm groups the new formulation provides a reduction close to one order of magnitude both in computational cost and memory requirements with a moderate impact on the accuracy of the solution

error analysis for the numerical evaluation of the diagonal forms of the scalar spherical addition theorem the numerical solution of wave scattering from large objects or from a large cluster of scatterers requires excessive computational resources and it becomes necessary to use approximate but fast methods such as the fast multipole method however since these methods are only approximate it is important to have an estimate for the error introduced in such calculations an analysis of the error for the fast multipole method is presented and estimates for truncation and numerical integration errors are obtained the error caused by polynomial interpolation in a multilevel fast multipole algorithm is also analyzed the total error introduced in a multilevel implementation is also investigated numerically

truncation error analysis of multipole expansion the multilevel fast multipole algorithm is based on the multipole expansion which has numerical error sources such as truncation of the addition theorem numerical integration and interpolation anterpolation of these we focus on the truncation error and discuss its control precisely the conventional selection rule fails when the buffer size is small compared to the desired numerical accuracy we propose a new approach and show that the truncation error can be controlled and predicted regardless of the number of buffer sizes

solution to the full vectorial 3 d inverse source problem by multilevel fast multipole method inspired hierarchical disaggregation a 3 d imaging approach based on a multilevel fast multipole method inspired hierarchical disaggregation of the broadband plane wave spectrum is introduced to solve the full vectorial electromagnetic inverse source problem based on the knowledge of the radiated fields in terms of complexity this algorithm is identical to fast fourier transform accelerated 3 d imaging techniques in terms of applicability the hierarchical disaggregation is advantageous for commonly encountered spherical k space data since the method can be directly combined with the near field fast multipole translations both far and near field data can be handled conveniently the investigation includes an analysis of the inherent point spread function and numerical results

interaction properties of complex modified korteweg de vries mkdv solitons abstract interaction properties of complex solitons are studied for the two u 1 invariant integrable generalizations of the modified korteweg de vries mkdv equation given by the hirota equation and the sasa satsuma equation which share the same traveling wave single soliton solution having a sech profile characterized by a constant speed and a constant phase angle for both equations nonlinear interactions in which a fast soliton collides with a slow soliton are shown to be described by 2 soliton solutions that can have three different types of interaction profile depending on the speed ratio and the relative phase angle of the individual solitons in all cases the shapes and speeds of the solitons are found to be preserved apart from a shift in position such that their center of momentum moves at a constant speed moreover for the hirota equation the phase angles of the fast and slow solitons are found to remain unchanged while for the sasa satsuma equation the phase angles are shown to undergo a shift such that the relative phase between the fast and slow solitons changes sign

note on interpolational basis functions in the method of moments em scattering efficient basis sets for the method of moments may be obtained using quasi localized bandlimited interpolational functions that broadly speaking are defined relative to a mean sampling rate that is adjusted to curvature and proximity to edges thus reflecting the local spatial frequency bandwidth computed scattering data in a number of structures including perfectly conducting circular and elliptical two dimensional cylinders as well as a flat infinite strip indicate that reasonable accuracy can be obtained with an average rate of between 2 5 and 3 basis functions per wavelength average sampling rates need not correspond strictly to the bandwidth of the basis functions and there is considerable latitude with respect to random variation of sampling intervals although each basis function typically extends over several sample points required integrals can be obtained speedily by the use of standard sampling theoretical methods

fourier pseudospectral solution of the regularised long wave equation abstract an algorithm is presented for the fourier pseudospectral solution of the regularised long wave rlw equation the semi discrete equations satisfy the energy conservation condition of the rlw equation numerical results are presented to show that the scheme can resolve the fine structure of wave interaction problems evidence is presented to show that the popular second order leap frog time discretisation will produce high accuracy only if the time step is well below the linear stability limit by considering linear and nonlinear models a case is made for the use of higher order accuracy in time

on landau s eigenvalue theorem and information cut sets a variation of landau s eigenvalue theorem describing the phase transition of the eigenvalues of a time frequency limiting self adjoint operator is presented the total number of degrees of freedom of square integrable multidimensional bandlimited functions is defined in terms of kolmogorov s n width and computed in some limiting regimes where the original theorem cannot be directly applied results are used to characterize up to order the total amount of information that can be transported in time and space by multiple scattered electromagnetic waves rigorously addressing a question originally posed in the early works of toraldo di francia and gabor applications in the context of wireless communication and electromagnetic sensing are discussed

reflector antenna fields an exact aperture like approach a new computational approach is presented which allows fast analysis of radiation from large reflector antennas for an aperture a fourier transform ft relationship does exist between far field and aperture distribution accordingly the far field can be exactly reconstructed from the knowledge of approximately one sample per lobe shannon whittaker theorem applied at nyquist rate the finite reflector curvature introduces an extra factor in the radiation integral so that the radiation integral is no longer a ft in order to overcome this difficulty a new pseudosampling expansion which explicitly takes into account the extra factor is developed for parabolic reflector the sampling functions are related to the fresnel integrals and the far field can be exactly reconstructed in terms of aperture far field samples which can be computed using the fast fourier transform fft numerical computations and error analysis show the excellent performance of the method which can be generalized to deal with arbitrary reflector surfaces and near field evaluation

rapid solution of integral equations of scattering theory in two dimensions abstract the present paper describes an algorithm for rapid solution of boundary value problems for the helmholtz equation in two dimensions based on iteratively solving integral equations of scattering theory cpu time requirements of previously published algorithms of this type are of the order n 2 where n is the number of nodes in the discretization of the boundary of the scatterer the cpu time requirements of the algorithm of the present paper are n 4 3 and can be further reduced making it considerably more practical for large scale problems

fast and accurate near field far field transformation by sampling interpolation of plane polar measurements an optimal sampling interpolation algorithm which allows the accurate recovery of plane rectangular near field samples from the knowledge of the plane polar ones is developed this enables the standard near field far field nf ff transformation which takes full advantage of the fast fourier transform fft algorithm to be applied to plane polar scanning the maximum allowable sample spacing is also rigorously derived and it is shown that it can be significantly greater than lambda 2 as the measurement place moves away from the source this allows a remarkable reduction of both measurement time and memory storage requirements the sampling approach is compared with that based on the bivariate lagrange interpolation bli method the sampling reconstruction agrees with the exact results significantly better than the bli in spite of the significantly lower number of required measurements

inelastic interaction of nearly equal solitons for the quartic gkdv equation this paper describes the interaction of two solitons with nearly equal speeds for the quartic gkdv equation partial tu partial x partial x 2u u 4 0 quad t x in mathbb r 0 1 we call soliton a solution of 0 1 of the form u t x qc x ct y0 where c 0 y0 and q c q c 4 cq c since 0 1 is not an integrable model the general question of the collision of two given solitons q c 1 x c 1 t q c 2 x c 2 t with c1 c2 is an open problem