symmetries of the kadomtsev petviashvili equation generalized symmetries with arbitrary functions of time t for the well known 2 1 dimensional integrable model kadomtsev petviashvili kp equation are found by means of the extended mastersymmetry approach then an explicit and simple constructive formula for the symmetries of the kp equation is derived directly from the symmetry definition equation without using complicated recursion operators all the known symmetries appear as special cases of those obtained in this paper the general infinite dimensional lie algebra constituted by these symmetries is also given

new exact solutions of the broer kaup equations in 2 1 dimensional spaces abstract with the aid of maple several new kinds of exact solutions for the broer kaup equations in 2 1 dimensional spaces are obtained by using a new ansatz this approach can also be applied to other nonlinear evolution equations

nonparametric trellis equalization in the presence of non gaussian interference we consider the problem of trellis equalization of the intersymbol interference channel in the presence of thermal noise and cochannel interference cci conventional maximum likelihood sequence estimation mlse and maximum a posteriori probability map trellis equalizers treat the sum of noise and interference as additive white gaussian noise while cci is generally a colored non gaussian process we propose a novel nonparametric approach based on the estimation of the probability density function of the noise plus interference given the availability of a limited volume of data the density is estimated by kernel smoothing techniques the use of a whitening filter in the presence of temporally colored disturbance is also addressed simulation results are provided for the global system for mobile communications gsm showing a significant performance improvement with respect to the equalizer based on the gaussian assumption major advantages of the proposed strategy are its intrinsic robustness and general applicability to those cases where accurate modeling of the interference is difficult or a model is not available

on sampling rate analog prefiltering and sufficient statistics for digital receivers we consider the joint sequence estimation timing and phase recovery for linear modulation the paper differs from the classical ones in the sense that time discrete algorithms suitable for fully digital receivers are discussed sufficient conditions are given such that the signal samples represent sufficient statistics these conditions involve signal bandwidth sampling symbol rate and the analog prefilter characteristics it is shown that the sampling rate need not be an exact multiple of the symbol rate i e the samples can be taken from a free running oscillator all subsequent signal processing operations in the receiver then operate with the clock of this free running oscillator timing recovery is then performed by a time variant linear digital interpolator and a decimator carrier recovery and sequence estimation are performed at an average rate of one symbol per sample the digital matched filter for this case is derived for an arbitrary colored noise spectrum

on the integrability of multidimensional nonlinear evolution equations the integrability test scheme of chen lee and liu h h chen y c lee and c s liu phys scr 20 490 1979 from one space dimension to multispace dimensions is generalized the temporal equation of the lax pair is still the linearized perturbed equation that defines the symmetries but the spectral operator in the lax pair is no longer the linear recursion operator for symmetries the absence of the linear recursion operator for symmetries in higher spatial dimensions therefore presents no direct obstacle to the chen lee liu test scheme the kadomtsev petviashvili equation is shown as an example

bi hamiltonian formulation of the kadomtsev petviashvili and benjamin ono equations it was shown recently that the kadomtsev petviashvili kp equation an integrable equation in 2 1 i e in two spatial and one temporal dimensions admits a bi hamiltonian formulation this was achieved by considering kp as a reduction of a 3 1 dimensional system in the variables x y1 y2 t it is shown here using the kp as a concrete example that equations in 2 1 possess two bi hamiltonian formulations and two recursion operators both hamiltonian operators associated with the x direction are local in contrast only one of the hamiltonian operators associated with the y direction is local furthermore using the benjamin ono equation as a concrete example it is shown that intergrodifferential equations in 1 1 admit an algebraic formulation analogous to that of equations in 2 1

lie point symmetry and some new soliton like solutions of the konopelchenko dubrovsky equations abstract in this paper the infinite dimensional symmetry groups of the 2 1 dimensional konopelchenko dubrovsky kd equation is found by the classical lie group method the symmetry groups are used to perform symmetry reduction and together with tanh function method we obtain soliton like solutions moreover a characterization of the corresponding lie algebra is given

conformal invariant expansion and high dimensional painleve integrable models a conformal invariant asymptotic expansion approach to solving real nonlinear physical systems is proposed in particular the 3 1 dimensional kadomtsev petviashvili 3dkp equation is solved approximately by using the conformal invariant asymptotic expansion in some special cases the approximate solutions of the 3dkp become exact many types of 3 1 dimensional painleve integrable models are obtained at the same time

special solutions from the variable separation approach the davey stewartson equation a variable separation procedure for the davey stewartson ds equation is proposed by using a prior ansatz to its bilinear form the reduced equations for two variable separated fields have the same trilinear form although they possess different independent variables the trilinear equation can be changed to a spacetime symmetric form and can be solved by means of a boussinesq type equation system whenever a pair of solutions of the reduced fields are obtained a corresponding solution of the ds equation can be obtained algebraically the single dromion solution and some kinds of positon solutions are obtained explicitly

exact evaluation of the collapse phase boundary for two dimensional directed polymers the phase boundary of the collapsed phase for a directed polymer on a square lattice in the presence of an attractive wall and monomer monomer interactions is calculated exactly using transfer matrix techniques the position of the multicritical point is also identified

interpolation in digital modems ii implementation and performance for pt i see ibid vol 41 no 3 p 502 208 1993 properties of a specific class of interpolators that are based upon polynomials are discussed several implementations are described one of which is particularly convenient in practical hardware simulations demonstrate that simple interpolators give excellent performance in many cases two point linear interpolation is adequate if better performance is needed classical four point third order polynomials could be used better yet a novel four point interpolating filter with piecewise parabolic impulse response can have performance superior to that of the standard cubic interpolator and still be implemented much more simply the nco based control method presented in part i is shown to be equivalent to a conventional phase locked loop and its operation is verified by simulation

non truncated formal series symmetries and generalized virasoro algebra akns type breaking soliton equation using the formal series symmetry approach we obtain three sets of generalized symmetries of the akns type breaking soliton equation these sets of formal series symmetries are not truncated except that the arbitrary functions of the formal series symmetries are fixed as polynomials of the corresponding independent variables differing from the truncated cases such as kp and toda field equations these non truncated symmetries constitute another type of generalization of the virasoro algebra

synchronized per survivor mlsd receiver using a differential kalman filter a synchronized per survivor processing psp maximum likelihood sequence detection mlsd receiver is presented for a fast frequency selective rayleigh fading channel and large carrier frequency offset it is shown that by incorporating the synchronization parameters the timing error carrier frequency and phase offsets into the channel impulse response cir and modifying the resulting state space model by a differential approach the time varying carrier frequency offset can be effectively tracked using a simple least mean square lms estimator new criteria are proposed based on the smoothness of the estimated channel derivatives new criteria are proposed based on this fact that for smoothly time varying cir and frequency offset the magnitude of the cir time derivative compared with the magnitude of cir should be very small it is illustrated that the new criteria and the conventional mean square error mse are complementary

joint maximum likelihood parameter estimation for burst ds spread spectrum transmission we first derive the joint optimal maximum likelihood ml estimator of the carrier phase both doppler shift and doppler rate and the spreading code delay for a short burst direct sequence spread spectrum ds ss transmission in the absence of the data modulation the typical burst duration is three data bit periods 60 ms the performance of the joint estimator is analytically derived separately for high and low carrier to noise ratio cnr values a suboptimal ml estimator based on the method of averaged periodogram is proposed for the data modulation present case allowing the joint estimation of the data bit values then the above parameters are assumed correctly estimated and a segmentation approach is adopted deriving the optimal joint ml estimator for the bit synchronization epoch and data simulations show the joint estimators perform reliable down to a cnr of approximately 30 db spl middot hz

generalized dromion solutions of the 2 1 dimensional kdv equation the rich dromion structures for a 2 1 dimensional kdv equation are revealed the dromions in a high dimensional integrable model may have a free shape in one or more directions multi dromion solutions can be driven by perpendicular line non perpendicular line and curved line ghost solitons

sampling and prefiltering effects on blind equalizer design in the development of equalization algorithms for unknown channels the effects of the sampling rate and the analog receive prefilter prior to discretization of the received signal are often overlooked in this paper these effects are investigated the relationship between the fractionally spaced output samples of a noise limiting prefilter and the symbol spaced output samples of a matched filter is studied for both the time invariant and the time varying channels it is shown that the prefilter and the sampling rate can have significant effects on blind equalization algorithms thus this paper provides a common framework for comparing different blind algorithms that are studied in the literature with different sampling rates a case study of the well known subspace method for blind channel identification is presented the effects of the noise color due to the prefilter on equalizers is investigated and the sensitivity of the truncation of the overall channel impulse response in terms of the mean squared error mse performance criterion is investigated through numerical examples

sequence detection in nonlinear channels a convenient alternative to analog predistortion a new maximum likelihood sequence detection receiver for spectrally efficient linear modulations on bandlimited bandpass nonlinear channels is proposed the receiver is based on oversampling the received signal corrupted by noise and nonlinear distortion contrary to other solutions in the literature in the proposed technique there is no need for a bank of matched filters and the receiver front end reduces to a single lowpass filter for a given peak power level a performance gain can be achieved over more traditional approaches to transmission on nonlinear channels such as those based on predistortion if a moderate spectral expansion is allowed to analyze the receiver performance the concept of distance spectrum is employed since the minimum distance alone cannot account for a reliable performance evaluation both analysis and simulation are carried out for realistic narrowband nonlinear channels possibly employing reduced state sequence detection appreciable gain margins are confirmed to be possible in these realistic cases

a systematic framework for iterative maximum likelihood receiver design in this paper we link the turbo principle to unconstrained maximum likelihood ml sequence detection and joint ml parameter estimation first we demonstrate for memoryless channels with complete channel state information how the turbo decoder can be systematically derived starting from the ml sequence detection criterion in particular we show that a method to solve the ml sequence detection problem is to iteratively solve the corresponding critical point equations of an equivalent unconstrained estimation problem by means of fixed point iterations the turbo decoding algorithm is obtained by approximating the overall a posteriori probabilities subsequently we show how this general approximative iterative maximum likelihood aiml framework can be applied to general iterative ml receiver design we consider static memoryless channels with unknown channel parameters the time selective fading channels with partial channel state information is the subject of a companion paper

joint design of interpolation filters and decision feedback equalizers this paper presents an algorithm to design jointly interpolation filters and decision feedback equalizers in the sense of minimum mean square error such that the joint capacity which is neglected in conventional design is explored to improve the receiver performance the algorithm comprises an iteration of two alternating simple quadratic minimizing operations and ensures convergence a simulation example for the raised cosine channel demonstrates that via this approach an improvement over the conventional design can be achieved

fast algorithms for discrete and continuous wavelet transforms several algorithms are reviewed for computing various types of wavelet transforms the mallat algorithm 1989 the a trous algorithm and their generalizations by shensa the goal of this work is to develop guidelines for implementing discrete and continuous wavelet transforms efficiently and to compare the various algorithms obtained and give an idea of possible gains by providing operation counts most wavelet transform algorithms compute sampled coefficients of the continuous wavelet transform using the filter bank structure of the discrete wavelet transform although this general method is already efficient it is shown that noticeable computational savings can be obtained by applying known fast convolution techniques such as the fft fast fourier transform in a suitable manner the modified algorithms are termed fast because of their ability to reduce the computational complexity per computed coefficient from l to log l within a small constant factor for large filter lengths l for short filters smaller gains are obtained fast running fir finite impulse response filtering techniques allow one to achieve typically 30 savings in computations

generalized symmetries and w infinity algebras in 3 dimensional toda field theory after establishing a formal theory for getting solutions of one type of high dimensional partial differential equation two sets of generalized symmetries of the 3d toda theory which arises from a particular reduction of the 4d self dual gravity equation are obtained concretely by a simple formula each set of symmetries constitutes a generalized w algebra which contains three types of the usual w algebras as special cases some open questions are discussed

symbolic computation and new families of exact soliton like solutions to the integrable broer kaup bk equations in 2 1 dimensional spaces in this paper new families of soliton like solutions are obtained for 2 1 dimensional integrable broer kaup equations by using the symbolic computation method developed by gao and tian sample solutions obtained from these methods are presented solitary wave solutions are merely a special case in one family the method can also be extended to other types of nonlinear evolution equations in mathematical physics

infinite dimensional symmetry algebras and an infinite number of conserved quantities of the 2 1 dimensional davey stewartson equation an infinite dimensional symmetry algebra of the davey stewartson equation is explicitly presented it is shown that this algebra is a gauge generalization of the symmetry transformation for the schrodinger equation and that the virasoro algebra appears as the subalgebra an infinite number of conserved quantities associated with the transformations are also obtained

2 1 dimensional m n component akns system painleve integrability infinitely many symmetries similarity reductions and exact solutions the 2 1 dimensional m n component akns system that is derived from the inner parameter dependent symmetry constraint of the kp equation is studied in detail first the painleve integrability of the model is proved by using the standard wtc and kruskal approach using the formal series symmetry approach the generalized kmv symmetry algebra and the related symmetry group are found the two dimensional similarity partial differential equation reductions and the ordinary differential equation reductions are obtained from the generalized kmv symmetry algebra and the direct method abundant localized coherent structures are revealed by the variable separation approach some special types of the localized excitations like the multiple solitoffs dromions lumps ring solitons breathers and instantons are plotted also

on a new hierarchy of symmetries for the kadomtsev petviashvili equation abstract we present a new hierarchy of symmetries for the kadomtsev petviashvili equation these new symmetries depend on the space and time variables explicitly together with the previously known classical symmetries they constitute an infinite dimensional lie algebra

a maximum likelihood digital receiver using coordinate ascent and the discrete wavelet transform in this paper a maximum likelihood ml method is presented for joint estimation of amplitude phase time delay and data symbols in a single user direct sequence spread spectrum communication system since maximization of the likelihood function is analytically intractable a novel coordinate ascent algorithm is used to obtain sequential updates of the data symbols and all unknown nuisance parameters the novelty of the algorithm is due to the use of a multiresolution expansion of the received signal and the use of polynomial rooting in the complex plane in place of a line search over the signal delay parameter the multiresolution structure of the algorithm is exploited to reduce sensitivity to impulsive noise via wavelet thresholding computer simulations of the single user system show that the algorithm has fast convergence and comparison with theoretical lower bounds establishes that the algorithm achieves nearly optimal error performance

lie symmetry reductions and exact solutions of some differential difference equations in this paper a class of differential difference equations ddes are considered for lie group analysis with the help of symbolic computation mathematica the continuous lie point symmetry technique is extended to obtain corresponding infinitesimals similarity reductions are derived by solving the characteristic equations then some exact solutions are presented by using inverse transformations in addition starting from concrete realization of the generalized virasoro type symmetry algebra f1 f2 f 1f2 f1f 2 many high dimensional ddes can be derived for example we give out the 2 1 dimensional toda lattice modified toda lattice and special toda lattice in a uniform way

a generalized f expansion method with symbolic computation exactly solving broer kaup equations abstract in this paper a generalized f expansion method is applied to construct exact solutions of the 2 1 dimensional broer kaup equations as a result many general exact non travelling wave and coefficient function solutions are obtained including single and combined non degenerate jacobi elliptic function solutions soliton like solutions and trigonometric function solutions each of which contains two arbitrary functions compared with most existing f expansion methods the proposed method gives new and more general exact solutions more importantly with the aid of symbolic computation the method provides a powerful mathematical tool to solve a large many nonlinear partial differential equations

symbol synchronization using signal samples and interpolation a method for symbol synchronization using two unsynchronized signal samples per symbol is presented signal values between the sample points are calculated by interpolation and then processed digitally to find a suitable strobe point the interpolated value at the strobe point is used for data detection or input to an equalizer simulations show that low variance timing estimates can be made for pulses with raised cosine spectra degraded by quadratic delay distortion

on the infinite dimensional symmetry group of the davey stewartson equations the lie algebra of the group of point transformations leaving the davey stewartson equations dse s invariant is obtained the general element of this algebra depends on four arbitrary functions of time the algebra is shown to have a loop structure a property shared by the symmetry algebras of all known 2 1 dimensional integrable nonlinear equations subalgebras of the symmetry algebra are classified and used to reduce the dse s to various equations involving only two independent variables

ergodic properties of microcanonical observables the problem of the existence of a strong stochasticity threshold in the fpu model is reconsidered using suitable microcanonical observables of thermodynamic nature like the temperature and the specific heat explicit expressions for these observables are obtained by exploiting rigorous methods of differential geometry measurements of the corresponding temporal autocorrelation functions locate the threshold at a finite value of the energy density which is independent of the number of degrees of freedom

design of optimal interpolation filter for symbol timing recovery we propose an optimal interpolation filter for symbol timing recovery in a digital receiver where the input analog to digital a d conversion sampling clock is not synchronized to the transmitter symbol clock the optimal filter is designed by minimizing the mean square error mse at the output of the receiver assuming that the correct timing difference between the nonsynchronized input samples and the correct strobe synchronized to the symbol is given the mse minimization procedure results in a system of linear equations which can easily be solved to yield the optimal filter coefficients we also analyze the symbol tracking performance of a symbol synchronizer that employs the proposed optimal interpolation filter although the proposed optimal filter is designed assuming the availability of the correct timing difference we show that it minimizes the timing estimation error variance even when the computed timing difference values deviate from the ideal we also show that the timing estimation is virtually unbiased if the length of the interpolation filter is greater than or equal to 4 simulation results are included to show the performance improvement realizable by employing the optimal interpolation filter

on the direct construction of the inverse scattering operators of integrable nonlinear hamiltonian systems abstract we show that the mere knowledge of a single symmetry propagator would suffice to construct the lax operators for the inverse scattering scheme associated with an integrable physical system with one spatial dimension this construction supplements in an important way the integrability test scheme of chen lee and liu a discussion about the feasibility of the above scheme to the integrable systems with higher spatial dimensions is also presented

an ekf based joint estimator for interference multipath and code delay in a ds spread spectrum receiver in direct sequence ds spread spectrum communications it is often necessary to obtain pseudo noise pn code synchronization in the presence of both narrowband interference and frequency selective multipath however conventional delay lock code tracking loops are not optimized for such applications nor are they well suited to digital implementations a code tracking algorithm based on the extended kalman filter ekf is described that provides both code synchronization and joint estimates of interferer and channel parameters it is first assumed that the interference can be modeled by an n th order autoregressive ar process and the multipath by a finite impulse response filter a composite channel equivalent to the convolution of the prewhitening filter and multipath coefficients is then constructed the received waveform is shown to be a linear function of the composite channel parameters that can therefore be directly estimated by an extended kalman filter the code delay spl tau is viewed as a nonlinear parameter that can likewise by estimated after an appropriate linearization using the ekf the performance of the algorithm is first evaluated by computing the average bit error rate ber of a digital rake receiver that employs the joint delay channel and interferer estimates derived from the ekf in addition a nonlinear analysis of the ekf is performed in which the code delay error and error covariance are modeled as a two dimensional markov process the joint probability density function of these parameters and nonlinear delay error variance are obtained via numerical integration of a two dimensional chapman kolmogorov equation

curvature torsion microcanonical density and stochastic transition we introduce geometrical indicators frenet serret curvature and torsion together with microcanonical density to give evidence to the stochastic transition of classical hamiltonian models fermi pasta ulam and lennard jones systems when the specific energy grows the transition is clearly detected through the breakdown of the harmonic like behaviour in combination with the vanishing of the dependence on the initial conditions this method of analysis presents both experimental and theoretical advantages it is fast and gives relatively sharp answers for the transition moreover a new insight is allowed on the deformations and the destruction of invariant surfaces in the ordered regime among the results it is noteworthy that going from 32 to 4096 degrees of freedom the stochastic transition depends only on the specific energy and not on the number of degrees of freedom

revisitation of the localized excitations of the 2 1 dimensional kdv equation in a previous paper lou s y 1995 j phys a math gen 28 7227 a generalized dromion structure was revealed for the 2 1 dimensional kdv equation which was first derived by boiti et al boiti m leon j j p manna m and pempinelli f 1986 inverse problems 2 271 using the idea of the weak lax pair in this paper using a backlund transformation and the variable separation approach we find there exist much more abundant localized structures for the 2 1 dimensional kdv equation the abundance of the localized structures of the model is introduced by the entrance of an arbitrary function of the seed solution some special types of dromion solution lumps breathers instantons and the ring type of soliton are discussed by selecting the arbitrary functions appropriately the dromion solutions can be driven by sets of straight line and curved line ghost solitons the dromion solutions may be located not only at the cross points of the lines but also at the closed points of the curves the breathers may breathe both in amplitude and in shape

nearly separable behavior of fermi pasta ulam chains through the stochasticity threshold for the periodic fermi pasta ulam chain with quartic potential we prove the relation p k 2 t 1 k 2 q k 2 i e the proportionality already at early timest between averaged kinetic and harmonic energies of each mode the factor depends on the parameters of the model but not on the mode and the number of degrees of freedom it grows with the anharmonic strength from the value 0 of the harmonic limit virial theorem up to few units for the system much above the threshold in the stochastic regime the time necessary to reduce the fluctuations ink to a fixed percentage remains at least one order of magnitude smaller than the time necessary to reach a similar level of equipartition the persistence of such a behavior even above the stochasticity threshold clarifies a number of previous numerical results on the relaxation to equilibrium e g the existence of several time scales and the relevance of the harmonic frequency spectrum the difficulties in the numerical simulation of the thermodynamic limit are also discussed

a bpsk qpsk timing error detector for sampled receivers a simple algorithm for detection of timing error of a synchronous band limited bpsk or qpsk data stream is proposed the algorithm requires only two samples per symbol for its operation one of the two samples is also used for the symbol decision derivation of the s curve reveals a sinusoidal shape

iterative multiuser receivers for cdma channels an em based approach maximum likelihood detection for the multiuser code division multiple access cdma channel is prohibitively complex this paper considers new iterative multiuser receivers based on the expectation maximization em algorithm and related more powerful space alternating algorithms the latter algorithms include the sage algorithm and a new missing parameter space alternating algorithm that alternately updates individual parameter components or treats them as probabilistic missing data application of these em based algorithms to the problem of discrete parameter estimation i e data detection in the gaussian multiple access channel leads to a variety of convergent receiver structures that incorporate soft decision feedback for interference cancellation and or sequential updating of iterative bit estimates convergence and performance analyses are based on well known properties of the em algorithm and on numerical simulation

infinitely many symmetries of the davey stewartson equation using a formal series symmetry method for the davey stewartson equation dse we find that there exist two sets of infinitely many formal series symmetries of the dse however different from the kadomtsev petviashvili equation kpe we failed to get infinitely many truncated symmetries only six truncated symmetries can be obtained simply from the formal series symmetries

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

modified cramer rao bounds for continuous phase modulated signals we consider the estimation of signal amplitude time offset and the parameters of a polynomial phase signal from a continuous phase modulated cpm signal that contains both unknown data symbols and known pilot symbols transformation of the polynomial phase signal into an orthogonal basis allows us to derive the modified cramer rao bounds mcrb for the problem of vector parameter estimation in closed form numerical results demonstrate that the achievable estimation accuracy significantly depends on the burst structure and highlight the need for properly designed pilot sequences since our bounds are easy to evaluate they can aid the design of pilot and burst configuration for cpm systems

the wavelet transform time frequency localization and signal analysis two different procedures for effecting a frequency analysis of a time dependent signal locally in time are studied the first procedure is the short time or windowed fourier transform the second is the wavelet transform in which high frequency components are studied with sharper time resolution than low frequency components the similarities and the differences between these two methods are discussed for both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time frequency density finally the notion of time frequency localization is made precise within this framework by two localization theorems

recursion operators and bi hamiltonian structures in multidimensions ii the algebraic properties of exactly solvable evolution equations in one spatial and one temporal dimensions have been well studied in particular the factorization of certain operators called recursion operators establishes the bi hamiltonian nature of all these equations recently we have presented the recursion operator and the bi hamiltonian formulation of the kadomtsev petviashvili equation a two spatial dimensional analogue of the korteweg devries equation here we present the general theory associated with recursion operators for bi hamiltonian equations in two spatial and one temporal dimensions as an application we show that general classes of equations which include the kadomtsev petviashvili and the davey stewartson equations possess infinitely many commuting symmetries and infinitely many constants of motion in involution under two distinct poisson brackets furthermore we show that the relevant recursion operators naturally follow from the underlying isospectral eigenvalue problems

source generation of the davey stewartson equation the source generation procedure sgp proposed by hu and wang inverse probl 22 1903 2006 provides a new way to systematically generate so called soliton equations with self consistent sources in this paper we apply this sgp to a davey stewartson ds equation based on the hirota bilinear form producing a system of equations which is called the ds equation with self consistent sources dsescs meanwhile we obtain the gramm type determinant solutions to the dsescs since the ds equation is a 2 1 dimensional integrable generalization of the nonlinear schrodinger nls equation the dsescs may be viewed as a 2 1 dimensional integrable generalization of the nonlinear schrodinger equation with self consistent sources these results indicate the commutativity of source generation procedure and 2 1 dimensional integrable generalizations for the nls equation

k symmetries and tau symmetries of evolution equations and their lie algebras on the basis of tu s work 1951 the author establishes a more general skeleton on k symmetries and tau symmetries of evolution equations and their lie algebraic structures and discuss carefully the corresponding symmetries and lie algebras for kdv and jaulent miodek hierarchies

2 1 dimensional models with virasoro type symmetry algebra according to a theory proposed in a previous paper by lou and hu 1994 starting from a realization of a virasoro type symmetry algebra we can obtain various 2 1 dimensional integrable models under the condition that the models possess the infinitely dimensional virasoro type symmetry algebra an explicit realization of the generalized virasoro type symmetry algebra is used to obtain concrete invariant models a set of equations which possesses the same infinite dimensional kac moody virasoro type lie point symmetry algebra as that of the kadomtsev petviashvilli equation is given

dromion like structures in a 3 1 dimensional kdv type equation dromion structures have been found in many 2 1 dimensional models the similar structure in 3 1 dimensions is studied in this paper for a kdv type equation starting from the bilinear form of the model we found that there are five types of multi dromion solutions for its potentials say the first type of multi dromion solution is driven by multi camber solitons with one of them being non parallel to the x axis the second third and fourth types of multi dromion solutions are driven by two camber solitons and one two and three sets of parallel plane solitons respectively the fifth type of multi dromion solution is driven by one set of parallel plane solitons one set of camber solitons which are parallel to the x axis and one camber soliton which is non parallel to the x axis phase shifts may be involved in the interactions among the multi dromions for the first and fifth types of solutions a single dromion solution of the model may possess quite a free shape for instance the point like dromions ring type dromions extended and sharp dromions and oscillatory dromions can be obtained by selecting some arbitrary functions appropriately

lie symmetries of hirota s bilinear equations the existence of lie point symmetries for a family of partial differential equations pdes written in hirota s bilinear formalism is investigated these equations have been studied in previous publications from the point of view of the existence of multisoliton solutions and also of the painleve property and are either known as integrable or good candidates for integrability for these equations the lie algebra of lie point symmetries is derived which in some cases turns out to be an infinite dimensional algebra