some new periodic solitary wave solutions of 3 1 dimensional generalized shallow water wave equation by lie symmetry approach abstract many important physical situations such as fluid flows marine environment solid state physics and plasma physics have been represented by shallow water wave equations in this article we construct new solitary wave solutions for the 3 1 dimensional generalized shallow water wave gsww equation by using optimal system of lie symmetry vectors the governing equation admits twelve lie dimension space a variety of analytic closed form solutions such as new periodic solitary wave cross kink soliton and doubly periodic breather type solutions have been obtained by using invariance of the concerned 3 1 dimensional gsww equation under one parameter lie group of transformations lie symmetry transformations have applied to generate the different forms of invariant solutions of the 3 1 dimensional gsww equation for different lie algebra lie symmetry method reduces 3 1 dimensional gsww equation into various ordinary differential equations odes while one of the lie algebra it is transformed into the well known 2 1 dimensional blmp equation it is affirmed that the proposed techniques are convenient genuine and powerful tools to find the exact solutions of nonlinear partial differential equations pdes under the suitable choices of arbitrary functions and parameters 2d 3d and contour graphics to the obtained results of gsww equation are also analyzed

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

enhanced multiple bit differential detection of doqpsk in this paper we consider multiple bit differential detection mbdd of differential offset quadrature phase shift keying doqpsk with conventional bit wise differential encoding de we propose two novel mbdd schemes that outperform simon s mbdd and approach the performance of coherent detection cd as the observation window size n increases the first scheme uses the full available detection window spanning n 1 bit intervals and is referred to as f mbdd a careful bit error rate ber analysis shows that a significant performance improvement can be realized by reducing the detection window size to n 3 bit intervals the resulting improved mbdd i mbdd of doqpsk with bit wise de achieves a similar performance as phoel s mbdd of doqpsk with more complex symbol wise de for both f mbdd and i mbdd tight upper bounds and accurate ber approximations are derived in addition since the complexity per bit decision of brute force decoding of mbdd of doqpsk grows exponentially with n we develop optimum and suboptimum fast decoding algorithms with complexities per bit decision of orders log n 1 and n respectively

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

n soliton solutions for shallow water waves equations in 1 1 and 2 1 dimensions abstract a variety of shallow water waves equations in 1 1 and 2 1 dimensions are investigated we first show that these models are completely integrable we next determine multiple soliton solutions for each equation the simplified hirota s bilinear method developed by hereman will be employed to achieve this goal a comparison between dispersion relations and the phase shifts will be conducted but possess the same coefficients for the polynomials of exponentials

multiple soliton solutions for the boussinesq equation 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 for the boussinesq equation the one soliton solutions will be handled by the tanh coth method the work highlights the significant features of the employed methods

two integrable lattice hierarchies and their respective darboux transformations two integrable lattice hierarchies associated with two discrete matrix spectral problems are derived and the infinitely many conservation laws of the first integrable model is obtained moreover the darboux transformations based on different darboux matrixes 2 3 4 and 3 2 4 for the above mentioned integrable hierarchies are established with the help of two different gauge transformations of lax pairs in this paper as an application the explicit solutions of the two integrable hierarchies are presented

generalization of exp function and other standard function methods exp function and other standard function methods for solving nonlinear differential equations are generalized in this paper an analytical criterion determining if a solution can be expressed in a form comprising standard functions is derived new computational algorithm for automatic identification of the structure of the solution is constructed the algorithm provides information if the solution can be expressed as a sum of standard functions a ratio of sums of standard functions or even a more complex algebraic form involving standard functions several examples are used to illustrate the proposed concept

the hirota s direct method and the tanh coth method for multiple soliton solutions of the sawada kotera ito seventh order equation abstract in this work the sawada kotera ito seventh order equation is studied the tanh coth method is applied to obtain soliton solution of this equation the hirota s direct method combined with the simplified hereman s method are applied to determine the n soliton solutions for this equation the study highlights the significant features of the employed methods and its capability of handling completely integrable equations

explicit solutions of the 2 1 dimensional akns shallow water wave equation with variable coefficients abstract using an improved direct reduction method we find the equivalence transformations of 2 1 dimensional akns shallow water wave equation with variable coefficients and obtain the corresponding relationship between explicit solutions of akns equation and those of the corresponding reduced equation in addition we get some new explicit solutions of akns equation by applying lie symmetry method

multiple front solutions for the burgers kadomtsev petviashvili equation abstract in this work we study a completely integrable dissipative equation the burgers equation is extended by using the sense of the kadomtsev petviashvili kp equation the new established burgers kp equation is studied by using the tanh coth method to obtain kink solutions and periodic solutions we also apply the powerful hirota s bilinear method to establish exact n soliton solutions for the derived integrable equation

multiple bit differential detection of offset qpsk analogous to multiple symbol differential detection of quadrature phase shift keying qpsk a multiple bit differential detection scheme is described for offset qpsk that also exhibits continuous improvement in performance with increasing observation interval being derived from maximum likelihood considerations together with the representation of differentially encoded offset qpsk as a continuous phase modulation the proposed scheme is purported to be the most power efficient scheme for such a modulation and detection method

exact travelling wave solutions for the dissipative 2 1 dimensional akns equation abstract this paper employs the theory of planar dynamical systems and undetermined coefficient method to study travelling wave solutions of the dissipative 2 1 dimensional akns equation by qualitative analysis global phase portraits of the dynamic system corresponding to the equation are obtained under different parameter conditions furthermore the relations between the properties of travelling wave solutions and the dissipation coefficient r of the equation are investigated in addition the possible bell profile solitary wave solution kink profile solitary wave solutions and approximate damped oscillatory solutions of the equation are obtained by using undetermined coefficient method error estimates indicate that the approximate solutions are meaningful based on above studies a main contribution in this paper is to reveal the dissipation effect on travelling wave solutions of the dissipative 2 1 dimensional akns equation

exact travelling wave solutions for the generalized nonlinear schrodinger gnls equation with a source by extended tanh coth sine cosine and exp function methods the capability of extended tanh coth sine cosine and exp function methods as alternative approaches to obtain the analytic solution of different types of applied differential equations in engineering mathematics has been revealed in this study the generalized nonlinear schrodinger gnls equation is solved by three different methods to obtain the single soliton solutions for the equation the extended tanh coth and sine cosine methods are used furthermore for this nonlinear evolution equation the exp function method is applied to derive various travelling wave solution results show that while the first two procedures easily provide a concise solution the exp function method provides a powerful mathematical means for solving nonlinear evolution equations in mathematical physics

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

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

new method for parameter estimation in probabilistic models minimum probability flow fitting probabilistic models to data is often difficult due to the general intractability of the partition function we propose a new parameter fitting method minimum probability flow mpf which is applicable to any parametric model we demonstrate parameter estimation using mpf in two cases a continuous state space model and an ising spin glass in the latter case mpf outperforms current techniques by at least an order of magnitude in convergence time with lower error in the recovered coupling parameters

traveling wave solutions u v to a generalized drinfel d sokolov system which satisfy u a1vm a0 abstract an analysis of the coupled generalized drinfel d sokolov equations u t 1 uu x 1 u xxx v x 0 and v t 2 uv x 2 v xxx 0 is performed in the case of traveling wave solutions u and v satisfying the condition u a 1 v m a 0 we are able to classify all such solutions in terms of the model parameters and we then discuss the planar dynamics of such solutions numerical solutions are obtained and discussed for a variety of parameter regimes such results are one possible generalization of those given by wu et al l wu s chen c pang traveling wave solutions for generalized drinfeld sokolov equations applied mathematical modeling 33 2009 4126 4130

new solitary wave solutions for two nonlinear evolution equations abstract in this paper multiple exp function method is employed to investigate exact multiple wave solutions for 2 1 dimensional potential kadomtsev petviashvili equation and 3 1 dimensional jimbo miwa equation not only already known multiple wave solutions are recovered but also several new or more general multiple wave solutions are obtained

the hirota s direct method for multiple soliton solutions for three model equations of shallow water waves abstract multiple soliton solutions for three model equations for shallow water waves are determined the three models are completely integrable the hirota bilinear method is used to determine multiple soliton solutions of sech squared type for these equations the tanh coth method is used to obtain single soliton solutions and other solutions for these three models the three models have different linear dispersion relations but possess the same coefficients for the polynomials of exponentials

two systems of two component integrable equations multiple soliton solutions and multiple singular soliton solutions abstract in this work we study two systems of two component integrable equations the cole hopf transformation and hirota s bilinear method are applied to emphasize the integrability of each system multiple soliton solutions and multiple singular soliton solutions are formally derived

approximate inference in boltzmann machines inference in boltzmann machines is np hard in general as a result approximations are often necessary we discuss first order mean field and second order onsager truncations of the plefka expansion of the gibbs free energy the bethe free energy is introduced and rewritten as a gibbs free energy from there a convergent belief optimization algorithm is derived to minimize the bethe free energy an analytic expression for the linear response estimate of the covariances is found which is exact on boltzmann trees finally a number of theorems is proven concerning the plefka expansion relating the first order mean field and the second order onsager approximation to the bethe approximation experiments compare mean field approximation onsager approximation belief propagation and belief optimization

multiple soliton solutions for the lax kadomtsev petviashvili lax kp equation a new completely integrable dispersive equation is derived the new equation is obtained by extending the lax fifth order equation using the sense of the kadomtsev petviashvili kp equation in extending the kdv equation the newly derived lax kadomtsev petviashvili lax kp equation is investigated by using the tanh coth method and the hirota bilinear method to derive single soliton solution and n soliton solutions respectively the study highlights the multiple soliton solutions of the derived completely integrable equation

analytical solutions to a generalized drinfel d sokolov equation related to dssh and kdv6 abstract analytical solutions to the generalized drinfel d sokolov gds equations u t 1 uu x 1 u xxx v x 0 and v t 2 uv x 2 v xxx 0 are obtained for various values of the model parameters in particular we provide perturbation solutions to illustrate the strong influence of the parameters 1 and 2 on the behavior of the solutions we then consider a miura type transform which reduces the gds equations into a sixth order nonlinear differential equation under the assumption that 1 under such a transform the gds reduces to the sixth order drinfel d sokolov satsuma hirota dssh equation also known as kdv6 in the very special case 1 2 the method of homotopy analysis is applied in order to obtain analytical solutions to the resulting equation for arbitrary 1 and 2 an error analysis of the obtained approximate analytical solutions is provided

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

pulse shaping for differential offset qpsk pulse shaping is examined as a means to improve the performance of a differential offset quadrature phase shift keying system in a bandwidth constrained environment through optimization with respect to a composite nyquist criterion the derived pulse shapes have comparable performance to a pi 4 differential quadrature phase shift keying in an additive white gaussian noise awgn channel and better performance in a hard limited awgn channel

trigonometric and hyperbolic type solutions to a generalized drinfel d sokolov equation abstract a class of trigonometric and hyperbolic type solutions to the generalized drinfel d sokolov gds equations u t 1 uu x 1 u xxx v x 0 and v t 2 uv x 2 v xxx 0 is obtained for the case in which 2 0 for various values of the other model parameters the method of homotopy analysis is then applied to obtain local analytical solutions for nonzero values of the parameter 2 in effect extending the exact solutions we do not assume traveling wave solution forms for the analytical solutions that is we solve the generalized drinfel d sokolov equations as pdes without resorting to transforming the system to odes an error analysis of the obtained approximate local analytical solutions is provided then we outline a general framework by which one many construct solutions in either sine cosine or sinh cosh basis we provide the general perturbation expansion via homotopy analysis and we also discuss a method of selecting the convergence control parameter so as to minimize residual errors travelling solutions with time dependent amplitude are then discussed

frobenius integrable decompositions of nonlinear evolution equations with modified term frobenius integrable decompositions are introduced for nonlinear evolution equations with modified term two classes of polynomial equations with modified term are transformed into frobenius integrable ordinary differential equations by two special backlund transformations the resulting solutions are illustrated to describe the solution phenomena shared with the mkdv equation sharma tasso olver equation the modified kawachara equation the fifth order kdv equation and its various forms

parameter inference in a probabilistic model from data regulation of transition rate in the monte carlo method abstract we consider the inference of parameters in a probabilistic model from a data set which is generated by an unknown probabilistic model the monte carlo method is a tool for obtaining a data set obeying a given probability distribution a set of transition rates is required to satisfy three conditions irreducible aperiodic and stationary for a sampled data set to represent a probability distribution we utilize the stationary condition of a probability distribution with respect to transition rates to infer parameters a frequency distribution by a data set substitutes for an unknown probability distribution in the condition our method includes minimum probability flow as a special case and becomes superior to it as the number of samples increases

multiple soliton solutions of two extended model equations for shallow water waves abstract multiple soliton solutions for two extensions of model equations for shallow water waves presented in m j ablowitz d j kaup a c newell h segur the inverse scattering transform fourier analysis for nonlinear problems stud appl math 53 1974 249 315 r hirota j satsuma n soliton solutions of model equations for shallow water waves j phys soc jpn 40 2 1976 611 612 are obtained the two extensions possess identical dispersion relations but with different structures for the n soliton solutions for n 1 the hirota bilinear method is used to determine multiple soliton solutions of sech squared type for these extended equations the tanh coth method is used to obtain single soliton solutions

solitary wave solutions of the generalized shallow water wave gsww equation by hirota s method tanh coth method and exp function method abstract the generalized short wave equation gsww is studied by three distinct methods the hirota s bilinear method is used to derive multiple soliton solutions for the completely integrable forms of the gsww equation the tanh coth method is used to obtain single soliton solutions for this equation the exp function method is also applied to derive a variety of travelling wave solutions with distinct physical structures for this non linear evolution equation

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

the tanh coth and the sine cosine methods for kinks solitons and periodic solutions for the pochhammer chree equations abstract in this paper the tanh coth method and the sine cosine method are used for a reliable treatment of the pochhammer chree equations which include a variety of models travelling wave solutions of distinct structures namely bell shaped solitons kink shaped solitons and periodic solutions are formally derived the two methods demonstrate power reliability and efficiency

the cole hopf transformation and multiple soliton solutions for the integrable sixth order drinfeld sokolov satsuma hirota equation abstract the completely integrable sixth order nonlinear drinfeld sokolov satsuma hirota equation is studied three distinct methods namely the cole hopf transformation method the tanh coth method and the exp function method are used for a reliable treatment of this equation solitons multiple soliton solutions multiple singular soliton solutions and plane periodic solutions are obtained for this equations the study highlights the power of each method

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