on the mean field and classical limits of quantum mechanics the main result in this paper is a new inequality bearing on solutions of the n body linear schrodinger equation and of the mean field hartree equation this inequality implies that the mean field limit of the quantum mechanics of n identical particles is uniform in the classical limit and provides a quantitative estimate of the quality of the approximation this result applies to the case of c1 1 interaction potentials the quantity measuring the approximation of the n body quantum dynamics by its mean field limit is analogous to the monge kantorovich or wasserstein distance with exponent 2 the inequality satisfied by this quantity is reminiscent of the work of dobrushin on the mean field limit in classical mechanics func anal appl 13 115 123 1979 our approach to this problem is based on a direct analysis of the n particle liouville equation and avoids using techniques based on the bbgky hierarchy or on second quantization

the boltzmann grad limit of a hard sphere system analysis of the correlation error we present a quantitative analysis of the boltzmann grad low density limit of a hard sphere system we introduce and study a set of functions the correlation errors measuring the deviations in time from the statistical independence of particles propagation of chaos in the context of the bbgky hierarchy a correlation error of order k measures the event where k particles are connected by a chain of interactions preventing the factorization we show that provided k varepsilon alpha such an error flows to zero with the average density varepsilon for short times as varepsilon gamma k for some positive alpha gamma in 0 1 this provides an information on the size of chaos namely j different particles behave as dictated by the boltzmann equation even when j diverges as a negative power of varepsilon the result requires a rearrangement of lanford perturbative series into a cumulant type expansion and an analysis of many recollision events

new ideas for solving size structured population models the paper outlines new ideas for solving a class of models that describe the evolution of a size structured population the decomposition method to be presented avoids the cumbersome calculations of other approximation techniques some test models are investigated to illustrate the reliability and effectiveness of the proposed scheme

multivariate logistic models summary the multivariate logistic transform is a reparameterisation of cell probabilities in terms of marginal logistic contrasts it is known that an arbitrary set of logistic contrasts may not correspond to a valid joint distribution in this paper we present an efficient algorithm for detecting whether or not the inverse transform exists and for computing it if it does

binary models for marginal independence summary log linear models are a classical tool for the analysis of contingency tables in particular the subclass of graphical log linear models provides a general framework for modelling conditional independences however with the exception of special structures marginal independence hypotheses cannot be accommodated by these traditional models focusing on binary variables we present a model class that provides a framework for modelling marginal independences in contingency tables the approach that is taken is graphical and draws on analogies with multivariate gaussian models for marginal independence for the graphical model representation we use bidirected graphs which are in the tradition of path diagrams we show how the models can be parameterized in a simple fashion and how maximum likelihood estimation can be performed by using a version of the iterated conditional fitting algorithm finally we consider combining these models with symmetry restrictions

homotopy perturbation method for a type of nonlinear coupled equations with parameters derivative abstract in this paper homotopy perturbation method is directly extended to investigate nonlinear coupled equations with parameters derivative and to derive their numerical solutions these nonlinear coupled equations with parameters derivative contain many important mathematical physics equations and reaction diffusion equations by choosing different values of the parameters in general formal numerical solutions as a result a very rapidly convergent series solution is obtained the efficiency and accuracy of the method are verified by using two famous examples coupled burgers and mkdv equations numerical solutions show that good results have been achieved

convergent series solution of nonlinear equations abstract the author s decomposition method 1 provides a new efficient computational procedure for solving large classes of nonlinear and or stochastic equations these include differential equations containing polynomial exponential and trigonometric terms negative or irrational powers and product nonlinearities 2 also included are partial differential equations 3 delay differential equations 4 algebraic equations 5 and matrix equations 6 which describe physical systems essentially the method provides a systematic computational procedure for equations containing any nonlinear terms of physical significance the procedure depends on calculation of the author s a n a finite set of polynomials 1 13 in terms of which the nonlinearities can be expressed this paper shows important properties of the a n which ensure an accurate and computable convergent solution by the author s decomposition method 1 since the nonlinearities and or stochasticity which can be handled are quite general the results are potentially extremely useful for applications and make a number of common approximations such as linearization unnecessary

analytical solution of the linear fractional differential equation by adomian decomposition method in this paper we consider the n term linear fractional order differential equation with constant coefficients and obtain the solution of this kind of fractional differential equations by adomian decomposition method with the equivalent transmutation we show that the solution by adomian decomposition method is the same as the solution by the green s function finally we illustrate our result with some examples

a new approach to the wave equation an application of the decomposition method abstract in the present paper the inhomogeneous wave equation is solved quickly easily and elegantly by adomian s decomposition method

the decomposition method applied to chandrasekhar h equation in this paper adomian s decomposition method is applied to the nonlinear chandrasekhar h equation the solution is expressed as an infinite series it is shown that two or three iterations are sufficient to obtain good approximation of the exact solution adomian s method has been illustrated by considering some particular cases of this nonlinear integral equation that are of physical interest

on the size of chaos in the mean field dynamics we consider the error arising from the approximation of an n particle dynamics with its description in terms of a one particle kinetic equation we estimate the distance between the j marginal of the system and the factorized state obtained in a mean field limit as n our analysis relies on the evolution equation for the correlation error rather than on the usual bbgky hierarchy the rate of convergence is shown to be o j 2 n in any bounded interval of time size of chaos as expected from heuristic arguments our formalism applies to an abstract hierarchical mean field model with bounded collision operator and a large class of initial data covering a stochastic jump processes converging to the homogeneous boltzmann and the povzner equation and b quantum systems giving rise to the hartree equation

a new iterative method to compute nonlinear equations the aim of this paper is to construct a new efficient iterative method to solve nonlinear equations the new method is based on the proposals of abbasbandy on improving the order of accuracy of newton raphson method s abbasbandy improving newton raphson method for nonlinear equations by modified adomian decomposition method applied mathematics and computation 145 2003 887 893 and on the proposals of babolian and biazar on improving the order of accuracy of adomian s decomposition method e babolian j biazar on the order of convergence of adomian method applied mathematics and computation 130 2002 383 387 the convergence of the new scheme is proved and at least the cubic order of convergence is established several examples are presented and compared to other methods showing the accuracy and fast convergence of this new method also it is shown in this paper that the modified adomian s method developed by babolian and biazar to solve nonlinear equations e babolian j biazar solution of nonlinear equations by modified adomian decomposition method applied mathematics and computation 132 2002 167 172 should be slightly modified due to the fact that convergence of adomian s method does not ensure convergence of the modified method an example illustrates this fact which unlike what is claimed by the authors does not converge with their method but with a simple different choice of the zero component becomes convergent

a new symbolic computational approach to singular initial value problems in the second order ordinary differential equations this paper presents a new symbolic algorithm to compute the singular initial value problem of second order ordinary differential equations using adomian decomposition method the algorithm has been implemented in the computer algebra system maple to facilitate the application of this method a number of examples are presented to demonstrate the computation efficiency of the program

a reliable technique for solving the wave equation in an infinite one dimensional medium in this paper the initial value problem of the one dimensional wave equation where the domain of the space variable is unbounded will be handled by using the reliable decomposition method the solution is obtained in the form of a rapid convergent power series with elegantly computable terms comparing the decomposition method we used with several other methods that have been advanced for solving this model shows that the new technique is reliable powerful and promising

a stochastic system of particles modelling the euler equations we consider a system of n spheres interacting through elastic collisions at a stochastic distance in the limit n for a suitable rescaling of the interaction parameters we prove that the one particle distribution function converges to a local maxwellian whose gross density velocity and temperature satisfy the euler equation

association models for a multivariate binary response models for a multivariate binary response are parameterized by univariate marginal probabilities and dependence ratios of all orders the w order dependence ratio is the joint success probability of w binary responses divided by the joint success probability assuming independence this parameterization supports likelihood based inference for both regression parameters relating marginal probabilities to explanatory variables and association model parameters relating dependence ratios to simple and meaningful mechanisms five types of association models are proposed where responses are 1 independent given a necessary factor for the possibility of a success 2 independent given a latent binary factor 3 independent given a latent beta distributed variable 4 follow a markov chain and 5 follow one of two first order markov chains depending on the realization of a binary latent factor these models are illustrated by reanalyzing three data sets foremost a set of binary time series on auranofin therapy against arthritis likelihood based approaches are contrasted with approaches based on generalized estimating equations association models specified by dependence ratios are contrasted with other models for a multivariate binary response that are specified by odds ratios or correlation coefficients

new exact traveling wave solutions of the 4 1 dimensional fokas equation abstract in this paper two distinct methods are applied to look for exact traveling wave solutions of the 4 1 dimensional nonlinear fokas equation namely the modified simple equation method msem and the extended simplest equation method esem some new exact traveling wave solutions involving some parameters are obtained the solitary wave solutions can be extracted by assigning special values of these parameters the obtained solutions show the simplicity and efficiency of the used approaches that can be applied for nonlinear equations as well as linear ones

a new approach to quantitative propagation of chaos for drift diffusion and jump processes this paper is devoted the study of the mean field limit for many particle systems undergoing jump drift or diffusion processes as well as combinations of them the main results are quantitative estimates on the decay of fluctuations around the deterministic limit and of correlations between particles as the number of particles goes to infinity to this end we introduce a general functional framework which reduces this question to the one of proving a purely functional estimate on some abstract generator operators consistency estimate together with fine stability estimates on the flow of the limiting nonlinear equation stability estimates then we apply this method to a boltzmann collision jump process for maxwell molecules to a mckean vlasov drift diffusion process and to an inelastic boltzmann collision jump process with stochastic thermal bath to our knowledge our approach yields the first such quantitative results for a combination of jump and diffusion processes

a new approach to nonlinear partial differential equations abstract the author s decomposition method for the solution of operator equations which may be nonlinear and or stochastic is generalized to multidimensional cases

a new modification of the adomian decomposition method for linear and nonlinear operators in this paper we present an efficient modification of the adomian decomposition method that will facilitate the calculations we then conduct a comparative study between the new modification and the modified decomposition method the study is conducted through illustrative examples the new modification introduces a promising tool for many linear and nonlinear models

marginal regression analysis of a multivariate binary response we propose the use of the mean parameter for regression analysis of a multivariate binary response we model the association using dependence ratios defined in terms of the mean parameter the components of which are the joint success probabilities of all orders this permits flexible modelling of higher order associations using maximum likelihood estimation we reanalyse two data sets one with variable cluster size and the other a longitudinal data set with constant cluster size

the grad limit for a system of soft spheres a model describing the dynamics of a system of soft spheres is introduced the model contains a random mechanism which mollifies the deterministic model of hard sphere molecules it allows a rigorous deduction of the corresponding boltzmann equation for a wide class of initial data and arbitrarily long times

kac s program in kinetic theory this paper is devoted to the study of propagation of chaos and mean field limits for systems of indistinguishable particles undergoing collision processes the prime examples we will consider are the many particle jump processes of kac and mckean kac in proceedings of the third berkeley symposium on mathematical statistics and probability 1954 1955 vol iii pp 171 197 1956 mckean in j comb theory 2 358 382 1967 giving rise to the boltzmann equation we solve the conjecture raised by kac proceedings of the third berkeley symposium on mathematical statistics and probability 1954 1955 vol iii pp 171 197 1956 motivating his program on the rigorous connection between the long time behavior of a collisional many particle system and the one of its mean field limit for bounded as well as unbounded collision rates

the homogeneous boltzmann hierarchy and statistical solutions to the homogeneous boltzmann equation an existence and uniqueness result for the homogeneous boltzmann hierarchy is proven by exploiting the statistical solutions to the homogeneous boltzmann equation

latent variable models for longitudinal data with bivariate ordinal outcomes we use the concept of latent variables to derive the joint distribution of bivariate ordinal outcomes and then extend the model to allow for longitudinal data specifically we relate the observed ordinal outcomes using threshold values to a bivariate latent variable which is then modelled as a linear mixed model random effects terms are used to tie all together repeated observations from the same subject the cross sectional association between the two outcomes is modelled through the correlation coefficient of the bivariate latent variable conditional on random effects assuming conditional independence given random effects the marginal likelihood under the missing data at random assumption is approximated using an adaptive gaussian quadrature for numerical integration the model provides fixed effects parameters that are subject specific but retain the population averaged interpretation when properly scaled this is particularly well suited for the situation in which population comparisons and individual level contrasts are of equal importance data from a psychiatric trial the fluvoxamine an antidepressant drug study are used to illustrate the methodology

on kac s chaos and related problems this paper is devoted to establish quantitative and qualitative estimates related to the notion of chaos as firstly formulated by m kac cite kac1956 in his study of mean field limit for systems of n undistinguishable particles as n to infty first we quantitatively liken three usual measures of it kac s chaos some involving the all n variables other involving a finite fixed number of variables the cornerstone of the proof is a new representation of the monge kantorovich wasserstein mkw distance for symmetric n particle probability measures in terms of the distance between the law of the associated empirical measures on the one hand and a new estimate on some mkw distance on probability measures spaces endowed with a suitable hilbert norm taking advantage of the associated good algebraic structure next we define the notion of it entropy chaos and it fisher information chaos in a similar way as defined by carlen et al cite ccllv we show that it fisher information chaos is stronger than it entropy chaos which in turn is stronger than it kac s chaos more importantly with the help of the hwi inequality of otto villani we establish a quantitative estimate between these quantities which in particular asserts that it kac s chaos plus it fisher information bound implies it entropy chaos we then extend the above quantitative and qualitative results about chaos in the framework of probability measures with support on the it kac s spheres revisiting cite ccllv and giving a possible answer to cite open problem 11 ccllv additionally to the above mentioned tool we use and prove an optimal rate local clt in l infty norm for distributions with finite 6 th moment and finite l p norm for some p 1 last we investigate how our techniques can be used without assuming chaos in the context of probability measures mixtures introduced by de finetti hewitt and savage in particular we define the level 3 fisher information for mixtures and prove that it is l s c and affine as that was done in cite rr for the level 3 boltzmann s entropy

sinc galerkin method for solving nonlinear boundary value problems the sinc galerkin method is used to approximate solutions of nonlinear problems involving nonlinear second fourth and sixth order differential equations with homogeneous and nonhomogeneous boundary conditions the scheme is tested on four nonlinear problems the results demonstrate the reliability and efficiency of the algorithm developed

numerical study of modified adomian s method applied to burgers equation the application of adomian s decomposition method to partial differential equations when the exact solution is not reached demands the use of truncated series but the solution s series may have small convergence radius and the truncated series may be inaccurate in many regions in order to enlarge the convergence domain of the truncated series pade approximants pas to the adomian s series solution have been tested and applied to partial and ordinary differential equations with good results in this paper pas both in x and t directions applied to the truncated series solution given by adomian s decomposition technique for burgers equation are tested numerical and graphical illustrations show that this technique can improve the accuracy and enlarge the domain of convergence of the solution it is also shown in this paper that the application of adomian s method to the ordinary differential equations set arising from the discretization of the spatial derivatives by finite differences the so called method of lines may reduce the convergence domain of the solution s series

a cluster expansion approach to a one dimensional boltzmann equation a validity result we consider a stochastic particle system on the line and prove that when the number of particles diverges and the probability of a collision is suitably rescaled the system is well described by a one dimensional boltzmann equation the result holds globally in time without any smallness assumption

a comparison between adomian decomposition method and taylor series method in the series solutions in this work we will compare the performance of the adomian decomposition method and the taylor series method applied to the solution of linear and nonlinear ordinary differential equations the comparison shows that the decomposition method is reliable efficient and easy to use from a computational viewpoint although the two methods provide the solution in an infinite series the decomposition method provides a fast convergent series of easily computable components and eliminates cumbersome computational work needed by taylor series method

joint regression and association modeling of longitudinal ordinal data we propose models for longitudinal or otherwise clustered ordinal data the association between subunit responses is characterized by dependence ratios ekholm smith and mcdonald 1995 biometrika 82 847 854 which are extended from the binary to the multicategory case the joint probabilities of the subunit responses are expressed as explicit functions of the marginal means and the dependence ratios of all orders obtaining a computational advantage for likelihood based inference equal emphasis is put on finding regression models for the univariate cumulative probabilities and on deriving the dependence ratios from meaningful association generating mechanisms a data set on the effects of treatment with fluvoxamine which has been analyzed in parts before molenberghs kenward and lesaffre 1997 biometrika 84 33 44 is analyzed in its entirety selection models are used for studying the sensitivity of the results to drop out

stochastic particle approximations for generalized boltzmann models and convergence estimates fied boltzmann equation with general motion between collisions and nonlinear bounded jump collision operator and give the nonlinear martingale problem it solves we consider various linear interacting particle systems in order to approximate this nonlinear process we prove propagation of chaos in variation norm on path space with a precise rate of convergence using coupling and interaction graph techniques and a representation of the nonlinear process on a boltzmann tree no regularity nor uniqueness assumption is needed we then consider a nonlinear equation with both vlasov and boltzmann terms and give a weak pathwise propagation of chaos result using a compactness uniqueness method which necessitates some regularity these results imply functional laws of large numbers and extend to multitype models we give algorithms simulating or approximating the particle systems 1 framework and main results the boltzmann equation describes the evolution of the limit density f t x v of molecules of a rarefied gas at time t position x and speed v f is positive and f f t x v dx dv 1 it is given by

on product nonlinearities in stochastic differential equations the author s methods for solution of stochastic differential equations shown elsewhere to be applicable for nonlinear cases including polynomial exponential and trigonometric terms is shown to be applicable to product nonlinearities as well

adomian s method of decomposition critical review and examples of failure abstract adomian s method of decomposition is considered in application to initial boundary value problems for the one space dimensional spatially homogeneous heat conduction equation it is shown that the fundamental equation of the method is well defined only for certain restricted types of boundary conditions within the class of such boundary conditions examples are given such that the fundamental equation fails to have a unique solution and such that the sequence produced by iteration of this equation is divergent the latter is a counterexample to a published assertion of convergence

a derivation of the broadwell equation we consider a stochastic system of particles in a two dimensional lattice and prove that under a suitable limit i e n e 0 ne2 const wheren is the number of particles and e is the mesh of the lattice the one particle distribution function converges to a solution of the two dimensional broadwell equation for all times for which the solution of this equation exists propagation of chaos is also proven

numerical method for the solution of special nonlinear fourth order boundary value problems the sinc galerkin method is used to approximate solution of nonlinear problems this work deals with the sinc galerkin method for solving nonlinear fourth order differential equations with homogeneous and nonhomogeneous boundary conditions the scheme is tested on three nonlinear problems and a comparison with finite difference methods and fourth order multiderivative method is made it is shown that the sinc galerkin method yields better results

regression analysis of correlated ordinal data using orthogonalized residuals semi parametric regression models for the joint estimation of marginal mean and within cluster pairwise association parameters are used in a variety of settings for population averaged modeling of multivariate categorical outcomes recently a formulation of alternating logistic regressions based on orthogonalized marginal residuals has been introduced for correlated binary data unlike the original procedure based on conditional residuals its covariance estimator is invariant to the ordering of observations within clusters in this article the orthogonalized residuals method is extended to model correlated ordinal data with a global odds ratio and shown in a simulation study to be more efficient and less biased with regards to estimating within cluster association parameters than an existing extension to ordinal data of alternating logistic regressions based on conditional residuals orthogonalized residuals are used to estimate a model for three correlated ordinal outcomes measured repeatedly in a longitudinal clinical trial of an intervention to improve recovery of patients perception of altered sensation following jaw surgery

mean field dynamics singular potentials and rate of convergence we consider the time evolution of a system of n identical bosons whose interaction potential is rescaled by n 1 we choose the initial wave function to describe a condensate in which all particles are in the same one particle state it is well known that in the mean field limit n the quantum n body dynamics is governed by the nonlinear hartree equation using a nonperturbative method we extend previous results on the mean field limit in two directions first we allow a large class of singular interaction potentials as well as strong possibly time dependent external potentials second we derive bounds on the rate of convergence of the quantum n body dynamics to the hartree dynamics

necessary conditions for the appearance of noise terms in decomposition solutions series in this paper the phenomena of the noise terms that appear in the components of the series solution introduced by adomian and rach 1 will be examined extensively the phenomena is useful in demonstrating a fast convergence of the exact solution however the condition set by adomian and rach 1 in that these noise terms appear for every nonhomogeneous equation is not always true and the nonhomogeneity condition is not sufficient another necessary condition will be established in this study to ensure the appearance of noise terms in specific cases several differential and integral equations will be tested to confirm the newly developed condition

a new modification of adomian decomposition method for solving a kind of evolution equation in this paper we propose a new modification of adomian decomposition method for solving a kind of evolution equation the modification will improve the convergence of the series solution the validity of the modified technique is verified through illustrative examples

numerical solutions of coupled burgers equations with time and space fractional derivatives in this paper by introducing the fractional derivative in the sense of caputo the adomian decomposition method is directly extended to study the coupled burgers equations with time and space fractional derivatives as a result the realistic numerical solutions are obtained in a form of rapidly convergent series with easily computable components the figures show the effectiveness and good accuracy of the proposed method

the modified decomposition method for solving nonlinear algebraic equations in this paper an algorithm based on adomian s decomposition method is developed to approximate the solution of nonlinear algebraic equations the conditions of the convergence which depend on the coefficients of the equation are found the truncation error of the method is obtained special cases of the nonlinear algebraic equation are solved using the modified algorithm the presented work shows that the modified approach gives improvements over existing techniques

symbolic implementation of the algorithm for calculating adomian polynomials in this paper a symbolic implementation code is developed of a technique proposed by wazwaz appl math comput 111 2000 53 for calculating adomian polynomials for nonlinear operators the algorithm proposed by him appl math comput 111 2000 53 offers a promising approach for calculating adomian polynomials for all forms of nonlinearity but it is not easy to implement due to its huge size of algebraic calculations complicated trigonometric terms and unique summation rules it is well known that the algebraic manipulation language such as mathematica is useful to facilitate such a hard computational work pattern matching capabilities peculiar feature of mathematica are used in index regrouping which is a key role in constructing adomian polynomials the computer algebra software mathematica is used to collect terms to their order and to simplify the terms the symbolic implementation code author developed appearing at appendix has the flexibility that may easily cover any length of adomian polynomial for many forms of nonlinear cases a nonlinear evolution equation is investigated in order to justify the availability of symbolic implementation code

the analysis of longitudinal ordinal data with nonrandom drop out a model is proposed for longitudinal ordinal data with nonrandom drop out which combines the multivariate dale model for longitudinal ordinal data with a logistic regression model for drop out since response and drop out are modelled as conditionally independent given complete data the resulting likelihood can be maximised relatively simply using the em algorithm which with acceleration is acceptably fast and with appropriate additions can produce estimates of precision the approach is illustrated with an example such modelling of nonrandom drop out requires caution because the interpretation of the fitted models depends on assumptions that are unexaminable in a fundamental sense and the conclusions cannot be regarded as necessarily robust the main role of such modelling may be as a component of a sensitivity analysis

inversion of nonlinear stochastic operators abstract the operator theoretic method adomian and malakian j math anal appl 76 1 1980 183 201 recently extended adomian s solutions of nonlinear stochastic differential equations g adomian stochastic systems analysis in applied stochastic processes nonlinear stochastic differential equations j math anal appl 55 1 1976 441 452 on the modeling and analysis of nonlinear stochastic systems in proceeding international conf on mathematical modeling vol 1 pp 29 40 to provide an efficient computational procedure for differential equations containing polynomial exponential and trigonometric nonlinear terms n y the procedure depends on the calculation of certain quantities an and bn this paper generalizes the calculation of the an and bn to much wider classes of nonlinearities of the form n y y essentially the method provides a systematic computational procedure for differential equations containing any nonlinear terms of physical significance this procedure depends on a recurrence rule from which explicit general formulae are obtained for the quantities an and bn for any order n in a convenient form this paper also demonstrates the significance of the iterative series decomposition proposed by adomian for linear stochastic operators in 1964 and developed since 1976 for nonlinear stochastic operators since both the nonlinear and stochastic behavior is quite general the results are extremely significant for applications processes need not for example be limited to either gaussian processes white noise or small fluctuations

a new approach to the nonlinear advection problem an application of the decomposition method abstract in this paper the nonlinear advection problem is solved easily and elegantly by using the adomian s decomposition method the exact solution is quickly obtained by observing the appearance of the self canceling noise terms whose sum vanishes in the limit comparison with other existing techniques shows that the present approach is highly accurate

a learning approach to the two person decentralized team problem with incomplete information a learning approach to the two person decentralized team problem with incomplete information and with a 2x2 payoff matrix is considered it is shown that if the payoff matrix is unimodal there exists a proper choice of parameters of the learning algorithm that will ensure asymptotically an expected payoff as close to maximum payoff as desired it is shown that a team problem with multimodal payoff matrix gives rise to interesting class of open problems

exact solutions of the generalized 2 1 dimensional nonlinear evolution equations via the modified simple equation method in this paper the modified simple equation method msem is applied to construct exact solutions of the generalized 2 1 dimensional nonlinear evolution equations nlees involving parameters via the 2 1 dimensional calogero bogoyavlenskii schiff cbs equation the 2 1 dimensional breaking soliton equation and the 2 1 dimensional bogoyavlenskii s breaking soliton equation the solitary wave solutions are derived from the exact solutions by assigning special values of the parameters