design and implementation of two dimensional fully recursive digital filters the two dimensional 2 d fully recursive filter was recently introduced by the authors as a more general 2 d recursive filter in this paper we present a design algorithm and an implementation method for this class of filters the design algorithm incorporates a novel stability test we discuss the boundary condition problem which occurs in the implementation of fully recursive filters we propose a direct fully recursive implementation method which has been verified in software several design examples and comparisons are provided

chebyshev approximations for the direct design of 2 d quarter plane iir filters the development of various direct design techniques for inherently stable causal recursive two dimensional 2 d digital filters is described and illustrated by examples these techniques center around the development of 2 d z domain functions for use as arguments in the chebyshev function and provide for the design of low pass bandpass and high pass filters the specifications that can be prescribed are passband ripple filter order and normalized passband position parameters in addition to being inherently stable the filters possess an approximately flat group delay in most of the filter s passband a feature necessary for most applications

a search for bilinear equations passing hirota s three soliton condition ii mkdv type bilinear equations in this paper the results of a search for complex bilinear equations with two soliton solutions are presented the following basic types are discussed a the nonlinear schrodinger equation b dx g f 0 a dx dt f f gg and b the benjamin ono equation p dx f f 0 it is found that the existence of two soliton solutions is not automatic but introduces conditions that are like the usual three and four soliton conditions the search was limited by the degree of a 2 and by degree of p 4 the main results are the following 1 iad3x dxdt idy b g f 0 d2xf f gg 2 d2x ad2y idt b g f 0 dxdy f f gg 3 iad3x d2x idt f f 0 and 4 dxdt i adx bdt f f 0

the extended tanh method for new solitons solutions for many forms of the fifth order kdv equations abstract the extended tanh method is used to derive new solitons solutions for several forms of the fifth order nonlinear kdv equation the forms include the lax sawada kotera sk sawada kotera parker dye skpd kaup kupershmidt kk kaup kupershmidt parker dye kkpd and the ito equations the criteria established in a m wazwaz abundant solitons solutions for several forms of the fifth order kdv equation by using the tanh method appl math comput in press doi 10 1016 j amc 2006 02 047 to build up reliable relations between the parameters of the equation are confirmed by using this new approach entirely new bell shaped solitons are determined

an analytic study of fisher s equation by using adomian decomposition method in this paper we develop a framework to obtain exact solutions to fisher s equation and to a nonlinear diffusion equation of the fisher type by employing adomian decomposition method the proposed scheme is supported by examining nonlinear diffusion equations of the fisher type

exact wave solutions for a 3 1 dimensional generalized b type kadomtsev petviashvili equation abstract in this work we investigate a 3 1 dimensional generalized b type kadomtsev petviashvili equation based on the simplified hirota bilinear method we first construct its soliton solutions meanwhile we correct the formula of n soliton solution for this equation on the basis of these solitons we further calculate its lump solutions periodic waves meanwhile rogue waves as well as interaction solutions of this equation are also obtained by a direct algebraic method some figures are given to display the behavior of these solutions

nonlocal cauchy problems governed by compact operator families abstract we study the existence of mild solutions for the nonlocal cauchy problem u t au t f t u t t t 0 t 0 t u t 0 g u u 0 and give new criterions which extend some existing results in this area

the extended tanh method for abundant solitary wave solutions of nonlinear wave equations the extended tanh method is used to establish abundant solitary wave solutions of nonlinear wave equations the obtained solutions include solitons kinks and plane periodic solutions the study is an extension to the remarkable development by malfliet 1 the extended tanh method presents a wider applicability for handling nonlinear wave equations

global existence for semilinear evolution equations with nonlocal conditions abstract in this paper we study the global existence of solutions for semilinear evolution equations with nonlocal conditions via a fixed point analysis approach using the leray schauder alternative we derive conditions under which a solution exists globally

existence results and asymptotic behavior for nonlocal abstract cauchy problems the purpose of this paper is to study the existence and asymptotic behavior of solutions for cauchy problems with nonlocal initial datum generated by accretive operators in banach spaces

multiple front solutions for the burgers equation and the coupled burgers equations abstract in this work multiple front solutions for the burgers equation and the coupled burgers equations are examined the tanh coth method and the cole hopf transformation are used the work highlights the power of the proposed schemes and the structures of the obtained multiple front solutions

nonlinear variants of the improved boussinesq equation with compact and noncompact structures variants of the improved boussinesq equation with positive and negative exponents are investigated it is formally shown that these nonlinear variants give rise to compact and non compact physical structures where compactons solitons solitary patterns and periodic solutions are developed the presented sine cosine ansatz is reliable

the tanh coth method for solitons and kink solutions for nonlinear parabolic equations abstract the tanh coth method is used to derive solitons and kink solutions for some of the well known nonlinear parabolic partial differential equations the equations include the fisher equation newell whithead equation allen cahn equation fitzhugh nagumo equation fisher s equation and the burgers fisher equation the new tanh coth approach provides abundant solitons and kink solutions in addition to the existing ones the power of this manageable method is confirmed

existence of mild solutions for the semilinear nonlocal problem in banach spaces abstract in this paper we study the existence of mild solutions of the semilinear nonlocal initial value problem on a bounded and on an unbounded interval in our considerations we apply a new calculation method based on the technique of modulus of continuity in conjunction with idea of the family of measures of noncompactness in frechet space the results obtained in this paper generalize several ones obtained earlier by many authors

the interaction processes of the n soliton solutions for an extended generalization of vakhnenko equation the n soliton solutions for an extended generalization of vakhnenko equation are calculated by applying the improved hirota method and the variable transformations the n soliton solutions can be expressed explicitly furthermore the interaction processes are discussed for the n soliton solutions

resonant soliton and complexiton solutions for 3 1 dimensional boiti leon manna pempinelli equation abstract in this letter the linear superposition principle is used to discuss the 3 1 dimensional boiti leon manna pempinelli equation with bilinear derivatives as a result we obtain new resonant soliton and complexiton solutions by discussing two different cases involved the parameters these solutions are a class of n wave solutions of linear combinations of exponential traveling waves

nonlocal differential equations with multivalued perturbations in banach spaces abstract we discuss the existence of mild solutions for nonlocal differential inclusions with multivalued perturbations in banach spaces and establish new existence theorems for related cauchy problems which extend some existing results in this area using the established results we investigate a special nonlocal problem finally we also consider a partial functional differential equation

on the existence and asymptotic behaviour of solutions of an evolution equation and an application to the feynman kac theorem abstract in this paper we study the existence of mild solutions of a semilinear evolution equation on an unbounded interval the rapidity of the growth of those solutions is characterized moreover we investigate the local and global attractivity of solutions of an equation in question and we describe their asymptotic behaviour our investigations are conducted in a real separable banach space

existence and uniqueness of solutions to semilinear nonlocal parabolic equations abstract the banach contraction mapping theorem and the theory of analytic semigroups are used to prove the existence and uniqueness of solutions to nonlocal semilinear parabolic partial differential equations the equations consist of a parabolic boundary value problem and a relation connecting the initial value to values or weighted averages of values of the solution at other times

semilinear integrodifferential equations with nonlocal initial conditions abstract of concern is the cauchy problem for semilinear integrodifferential equations with nonlocal initial conditions under general and natural hypotheses we establish some new theorems about the existence and uniqueness of solutions for the cauchy problem as a consequence we unify and extend the corresponding theorems given previously for the cauchy problem for differential equations or integrodifferential equations with nonlocal initial conditions moreover we present two examples one of which comes from heat conduction in materials with memory to show that the existing results are not applicable to them in contrast with ours

symmetry reduction exact solutions and conservation laws of the sawada kotera kadomtsev petviashvili equation in this paper by applying a direct symmetry method we obtain the symmetry reduction group invariant solution and many new exact solutions of sk kp equation which include jacobi elliptic function solutions hyperbolic function solutions trigonometric function solutions and so on at last we also give the conservation laws of sk kp equation

variants of the two dimensional boussinesq equation with compactons solitons and periodic solutions variants of the two dimensional boussinesq equation with positive and negative exponents are studied the sine cosine ansatz is fruitfully used to carry out the analysis exact solutions of different physical structures compactons solitary patterns solitons and periodic solutions are obtained the quantitative change in the physical structure of the solutions is shown to depend mainly on the exponent of the wave function u x t and on the ratio a b of the derivatives of u x t

the tanh method a tool for solving certain classes of nonlinear evolution and wave equations the tanh or hyperbolic tangent method is a powerful technique to search for travelling waves coming out from one dimensional nonlinear wave and evolution equations in particular in those problems where dispersive effects reaction diffusion and or convection play an important role to show the strength of the method an overview is given to find out which kind of problems are solved with this technique and how in some nontrivial cases this method adapted to the problem at hand still can be applied single as well as coupled equations arising from wave phenomena which appear in different scientific domains such as physics chemical kinetics geochemistry and mathematical biology will be treated next attention is focussed towards approximate solutions as a result solitary and shock wave profiles are derived together with the associated width and velocity the same method can be easily extended so that difference differential equations can be similarly solved finally some extensions of the method are discussed

on classes of integrable systems and the painleve property the caudrey dodd gibbon equation is found to possess the painleve property investigation of the backlund transformations for this equation obtains the kuperschmidt equation a certain transformation between the kuperschmidt and caudrey dodd gibbon equation is obtained this transformation is employed to define a class of p d e s that identically possesses the painleve property for equations within this class backlund transformations and rational solutions are investigated in particular the sequences of higher order kdv caudrey dobb gibbon and kuperschmidt equations are shown to possess the painleve property

the hirota s bilinear method and the tanh coth method for multiple soliton solutions of the sawada kotera kadomtsev petviashvili equation abstract in this work we derive a new completely integrable dispersive equation the equation is obtained by combining the sawada kotera sk equation with the sense of the kadomtsev petviashvili kp equation the newly derived sawada kotera kadomtsev petviashvili sk kp equation is studied by using the tanh coth method to obtain single soliton solution and by the hirota bilinear method to determine the n soliton solutions the study highlights the significant features of the employed methods and its capability of handling completely integrable equations

existence of mild solutions for semilinear evolution equations with non local initial conditions abstract in this paper we study the existence of mild solutions for a class of semilinear evolution equations with non local initial conditions and extend some related results in this direction

a design method for two dimensional recursive digital filters a method for designing two dimensional symmetric half plane recursive digital filters is presented a filter is first designed as a parametrized family of one dimensional filters a simple approximation is then used to find a rational stable two dimensional filter some advantages and disadvantages of the method are discussed and several examples are given

multiple soliton solutions for the kp equation by hirota s bilinear method and by the tanh coth method abstract in this work we use the hirota s direct method combined with the simplified version of this method to determine the n soliton solutions n 1 2 3 4 5 for the kadomtsev petviashvili kp equation the one soliton solutions will be handled by the tanh coth method the work emphasizes the power of the two methods that will be used

mild solutions of semilinear evolution equation on an unbounded interval and their applications the aim of this paper is to give an existence theorem for a semilinear equation of evolution on an unbounded interval in the case when the generator of a semigroup depends on time parameter the considerations of this paper are based on the concept of a measure of noncompactness in frechet space and the classical tichonov fixed point principle moreover an application of the main theorem to the second order parabolic pde is given

the fully recursive filter a general 2 d recursive filter the conventional 2 d recursive filter can be thought of as performing a linear combination of 1 d filterings on past and present input and output data rows all of these component 1 d filters are fir except for that of the current output row in a fully recursive filter all the component 1 d filters are iir

nonlinear differential equations with nonlocal conditions in banach spaces abstract in this paper we study the existence of integral solutions for nonlinear differential equations with nonlocal initial conditions in banach spaces we derive conditions under which the integral solutions exist

the tanh method for traveling wave solutions of nonlinear equations in this work we employ the tanh method for traveling wave solutions of nonlinear equations the study is extended to equations that do not have tanh polynomial solutions the efficiency of the method is demonstrated by applying it for a variety of selected equations

uniqueness of solutions of parabolic semilinear nonlocal boundary problems abstract the purpose of the paper is to give two theorems about the uniqueness of solutions of parabolic semilinear nonlocal boundary problems the paper is a continuation of previous papers by byszewski and the generalization of some results from r rabczuk introduction to differential inequalities pwn warsaw 1976 polish j chabrowski on nonlocal problems for parabolic equations nagoya math j 93 1984 109 131 the theorems obtained in this paper can be applied in the theories of diffusion and heat conduction with better effects than the analogous theorems about parabolic initial boundary problems and than the analogous theorems about parabolic periodic boundary problems