a travelling wave solution to the kdv burgers equation in the present work by introducing a new potential function and by using the hyperbolic tangent method and an exponential rational function approach a travelling wave solution to the kdv burgers kdvb equation is presented it is observed that both methods lead to the same type of solution the solution method we introduced here is less restrictive and comprises some solutions existing in the current literature wave motion 11 1989 559 wave motion 14 1991 559

comment on application of exp function method for 3 1 dimensional nonlinear evolution equations comput math appl 56 2008 1451 1456 we show that boz and bekir a boz a bekir application of exp function method for 3 1 dimensional nonlinear evolution equations comput math appl 56 2008 1451 1456 obtained some incorrect solutions for the equations studied by means of the exp function method we verify our assertion by direct substitution and pole order analysis in addition we provide the correct results using the same approach

a note on the exp function method for traveling waves of nonlinear evolution equations abstract in this note we analyze the paper of noor et al 2010 1 using the exp function method noor et al found the generalized solitary and periodic solutions of zakharov kuznetsov and zakharov kuznetsov modified equal width equations we have checked noor s solutions and proved that seven from ten of them does not satisfy to equations considered the general solution of the zakharov kuznetsov equation in the traveling waves was obtained along ago we give this solutions in this letter for the reference source

a new note on exact complex travelling wave solutions for 2 1 dimensional b type kadomtsev petviashvili equation abstract exact solutions of the 2 1 dimensional kadomtsev petviashvili by zhang huiqun zhang a note on exact complex travelling wave solutions for 2 1 dimensional b type kadomtsev petviashvili equation appl math comput 216 2010 2771 2777 are considered to look for new types of exact solutions travelling wave solutions of equation zhang has used the g g expansion method we demonstrate that there is the general solution for the reduction by zhang from the 2 1 dimensional kadomtsev petviashvili equation and all solutions by zhang are found as partial cases from the general solution

abundant new exact solutions for the 3 1 dimensional jimbo miwa equation in this paper by using the generalized riccati equation mapping method and picking up its new solutions authors obtain abundant new exact solutions including kink solutions periodic form solutions soliton like solutions and rational solutions to a 3 1 dimensional jimbo miwa equation respectively

a level set method for imaging salt structures using gravity data abstractwe have developed a level set method for the inverse gravimetry problem of imaging salt structures with density contrast reversal under such a circumstance a part of the salt structure contributes two completely opposite anomalies that counteract with each other making it unobservable to the gravity data as a consequence this amplifies the inherent nonuniqueness of the inverse gravimetry problem so that it is much more challenging to recover the whole salt structure from the gravity data to alleviate the severe nonuniqueness it is reasonable to assume that the density contrast between the salt structure and the surrounding sedimentary host depends upon the depth only and is known a priori consequently the original inverse gravity problem reduces to a domain inverse problem where the supporting domain of the salt body becomes the only unknown we have used a level set function to parametrize the boundary of the salt body so that we reformulated the domain inverse problem into a nonlinear

modified extended tanh function method and its applications to nonlinear equations new exact travelling wave solutions for the generalized shallow water wave equation the improved boussinesq equation and the coupled system for the approximate equations for water waves are found using a modified extended tanh function method the obtained results include rational periodic singular and solitary wave solutions

a note on the g g expansion method abstract we demonstrate that the g g expansion method which is often used in finding exact solutions of nonlinear differential equation is equivalent to the well known tanh method and application of these methods gives the same exact solutions of nonlinear differential equations

a note on travelling wave solutions to lax s seventh order kdv equation ganji and abdollahzadeh d d ganji m abdollahzadeh appl math comput 206 2008 438 444 derived three supposedly new travelling wave solutions to lax s seventh order kdv equation each solution was obtained by a different method it is shown that any two of the solutions may be obtained trivially from the remaining solution furthermore it is noted that one of the solutions has been known for many years

linear inversion of gravity data for 3 d density distributions we have developed an improved levenburg marquart technique to rapidly invert bouguer gravity data for a 3 d density distribution as a source of the observed field this technique is designed to replace tedious forward modeling with an automatic solver that determines density models constrained by geologic information supplied by the user where such information is not available objective models are generated the technique estimates the density distribution within the source volume using a least squares inverse solution that is obtained iteratively by singular value decomposition using orthogonal decomposition of matrices with sequential householder transformations the source volume is subdivided into a series of right rectangular prisms of specified size but of unknown density this discretization allows the construction of a system of linear equations relating the observed gravity field to the unknown density distribution convergence of the solution to the system is tightly controlled by a damping pa

exact soliton solutions of the one dimensional complex swift hohenberg equation abstract using painleve analysis the hirota multi linear method and a direct ansatz technique we study analytic solutions of the 1 1 dimensional complex cubic and quintic swift hohenberg equations we consider both standard and generalized versions of these equations we have found that a number of exact solutions exist to each of these equations provided that the coefficients are constrained by certain relations the set of solutions include particular types of solitary wave solutions hole dark soliton solutions and periodic solutions in terms of elliptic jacobi functions and the weierstrass function although these solutions represent only a small subset of the large variety of possible solutions admitted by the complex cubic and quintic swift hohenberg equations those presented here are the first examples of exact analytic solutions found thus far

new kink shaped solutions and periodic wave solutions for the 2 1 dimensional sine gordon equation new exact solutions including the kink shaped solutions bell shaped solutions periodic solutions singular soliton solutions and rational solution for the 2 1 dimensional sine gordon equation are obtained using the tanh method the g g expansion method and the auxiliary function method respectively

pooling an experimental study of alternative testing and estimation procedures in a two way error component model abstract this paper considers a two way error component model with no lagged dependent variable and investigates the performance of various testing and estimation procedures applied to this model by means of monte carlo experiments the following results were found 1 the chow test performed poorly in testing the stability of cross section regressions over time and in testing the stability of time series regression across regions 2 the roy zellner test performed well and is recommended for testing the poolability of the data 3 the hausman specification test employed to test the orthogonality assumption gave a low frequency of type i errors 4 the lagrange multiplier test employed to test for zero variance components did well except in cases where it was badly needed 5 the problem of negative estimates of the variance components was found to be more serious in the two way model than in the one way model however replacing the negative variance estimates by zero did not have a serious effect on the performance of the second round gls estimates of the regression coefficients 6 as in the one way model all the two stage estimation methods performed reasonably well 7 better estimates of the variance components did not necessarily lead to better second round gls estimates of the regression coefficients

panel data models with spatially correlated error components abstract in this paper we consider a panel data model with error components that are both spatially and time wise correlated the model blends specifications typically considered in the spatial literature with those considered in the error components literature we introduce generalizations of the generalized moments estimators suggested in kelejian and prucha 1999 a generalized moments estimator for the autoregressive parameter in a spatial model international economic review 40 509 533 for estimating the spatial autoregressive parameter and the variance components of the disturbance process we then use those estimators to define a feasible generalized least squares procedure for the regression parameters we give formal large sample results for the proposed estimators we emphasize that our estimators remain computationally feasible even in large samples

on the extended applications of homogenous balance method in this paper we study the travelling wave reductions for certain 2 1 and 3 1 dimensional physically important nonlinear evolutionary equations by using the recently proposed homogenous balance method hbm through this analysis we explore certain new solutions for the equations we have studied

exact solitary wave solutions of nonlinear evolution and wave equations using a direct algebraic method the authors present a systematic and formal approach toward finding solitary wave solutions of nonlinear evolution and wave equations from the real exponential solutions of the underlying linear equations the physical concept is one of the mixing of these elementary solutions through the nonlinearities in the system the emphasis is however on the mathematical aspects i e the formal procedure necessary to find single solitary wave solutions by means of examples it is shown how various cases of pulse type and kink type solutions are to be obtained by this method an exhaustive list of equations so treated is presented in tabular form together with the particular intermediate relations necessary for deriving their solutions the extension of the technique to construct n soliton solutions and indicate connections with other existing methods is outlined

letter to the editor comment on new types of exact solutions for nonlinear schrodinger equation with cubic nonlinearity in this comment we analyze the paper abdelhalim ebaid s m khaled new types of exact solutions for nonlinear schrodinger equation with cubic nonlinearity j comput appl math 235 2011 1984 1992 using the traveling wave ebaid and khaled have found new types of exact solutions for nonlinear schrodinger equation with cubic nonlinearity we demonstrate that the authors studied the well known nonlinear ordinary differential equation with the well known general solution we illustrate that ebaid and khaled have looked for some exact solution for the reduction of the nonlinear schrodinger equation taking the general solution of the same equation into account

some applications of the g g expansion method to non linear partial differential equations in the present paper we construct the traveling wave solutions involving parameters of the 2 1 dimensional higher order broer kaup equations the 2 1 dimensional breaking soliton equations the 2 1 dimensional asymmetric nizhnik novikov vesselov equations and the 2 1 dimensional bkp equations in terms of the hyperbolic functions trigonometric functions and the rational functions by using a new approach namely the g g expansion method where g g x satisfies a second order linear ordinary differential equation when the parameters are taken special values the solitary waves are derived from the traveling waves the traveling wave solutions are expressed by the hyperbolic functions the trigonometric functions and the rational functions

on generalized loewner systems novel integrable equations in 2 1 dimensions a reinterpretation and generalization of a class of infinitesimal backlund transformations originally introduced in a gas dynamics context by loewner in 1952 leads to a linear representation for a novel class of 2 1 dimensional nonlinear equations the latter may be parametrized in terms of a triad of eigenfunctions moreover like the well known integrable davey stewartson and nizhnik novikov veselov equations the nonlinear systems typically contain the two spatial variables on an equal footing the dressing method is outlined for these generalized loewner systems it is noted that basic reductions lead to 2 1 dimensional versions of the principal chiral fields model toda lattice system and notably the classical sine gordon equation loewner systems on grassmannian the projective cpn and rpn manifolds are considered in particular the 2 1 dimensional integrable sine gordon system in which x and y occur in a symmetric manner arises naturally in this context a gauge equivalent system likewise eme

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

constrained inversion of gravity fields for complex 3 d structures as part of a research program to develop gravity interpretation tools that can be merged with seismic techniques a full 3 d complex structural inversion scheme for possibly multibody polyhedral models has been developed the forward modeling algorithm was adopted from previous work because the inverse problem is generally very ill posed several methods of regularizing the inversion were investigated and a combination of the most useful was adopted the combination includes i a structured matrix formulation for the system equations ii an analytical expression for the jacobian calculation iii first derivative damping iv a choice of damping parameter based on a variation of the trust region method v a weighted scheme for parameter correction and vi complete freezing of degrees of freedom found not to influence the gravity field significantly this combination yields a robust inversion which was successfully demonstrated on data over the galveston island salt dome offshore texas variat

adaptive learning 3d gravity inversion for salt body imaging we have developed an iterative scheme for inverting gravity data produced by salt bodies with density contrasts relative to the sediments varying from positive to negative crossing in this way the nil zone our inversion method estimates a 3d density contrast distribution through a piecewise constant function defined on a user specified grid of cells it consists of two nested iterative loops the outer loop uses an adaptive learning strategy that starts with a coarse grid of cells a set of first guess geometric elements axes and points and the corresponding assigned density contrasts from the second iteration on this strategy refines the grid and automatically creates a new set of geometric elements points only and associated density contrasts each geometric element operates as the first guess skeletal outline of a section of the salt body to be imaged the inner loop estimates the 3d density contrast distribution for the grid of cells and for the set of geometric elements defined in the oute

three dimensional gravity inversion using graph theory to delineate the skeleton of homogeneous sources abstractwe developed a new strategy based on graph theory concepts to invert gravity data using an ensemble of simple point masses our method consisted of a genetic algorithm with elitism to generate a set of possible solutions each estimate was associated to a graph to solve the minimum spanning tree mst problem to produce unique and stable estimates we restricted the position of the point masses by minimizing the statistical variance of the distances of an mst jointly with the data misfit function during the iterations of the genetic algorithm hence the 3d spatial distribution of the point masses identified the skeleton of homogeneous gravity sources in addition our method also gave an estimation of the anomalous mass of the source so together with the anomalous mass the skeleton could aid other 3d methods with promising geometric a priori parameters several tests with different values of regularizing parameter were made to bespeak this new regularizing strategy the inversion results ap

analytical properties and exact solutions of the lotka volterra competition system the lotka volterra competition system with diffusion is considered the painleve property of this system is investigated exact traveling wave solutions of the lotka volterra competition system are found periodic solutions expressed in terms of the weierstrass elliptic function are also given

time fractional 2 1 dimensional wu zhang system dispersion analysis similarity reductions conservation laws and exact solutions abstract this paper examines the time fractional 2 1 dimensional wu zhang system describing dispersive long waves the dispersion relation of waves has been obtained from linear analysis and used to find the phase and group velocity the dispersion relation shows an anomalous dispersion of waves lie symmetries and the corresponding similarity reductions are carried out using riemann liouville fractional derivative and the order of the system is reduced to lower dimension furthermore the system is analysed for nonlinear self adjointness and the conservation laws are obtained associated with infinitesimal symmetries by applying new conservation theorem the adjoint variables are used to convert conservation laws into original dependent variables the exponential rational function method is employed to find exact solutions revealing kink and bell type profiles the effect of fractional order on the wave profile of solutions is discussed graphically

the exp function method and generalized solitary solutions the exp function method is applied to a system of nonlinear partial differential equations and generalized solitary solutions with free parameters are obtained the solution procedure is simple with the help of symbolic computation

imaging geologic surfaces by inverting gravity gradient data with depth horizons the nonuniqueness problem that occurs when inverting potential field data is well known it can however be surmounted by jointly inverting these data with independent data sets incorporating depth information and regularizing the solution the goal is to produce a geologic model that is compatible with all measured quantities does not exceed any prescribed limits and is geologically plausible to achieve this we have developed a spatially based surface inversion algorithm that solves for the geometric interface between geologic bodies the bodies are constructed from grids of rectangular prisms that have their bottom depths adjusted by the algorithm to form the inverted surface to solve large scale inversions approximations are used in the potential field calculations that allow internal matrices to be stored in sparse format with minimal loss of accuracy the impetus for the work came from the need to combine airborne gravity gradient data with depth horizons estimated from interpreted 2d seismic

new travelling wave solutions to the ostrovsky equation in this work new travelling wave solutions to the ostrovsky equation are studied by employing the improved tanh function method with this method the ostrovsky equation is reduced to the nonlinear ordinary differential equation and then the different types of exact solutions are derived based on the solutions of the riccati equation we will compare our solutions with those gained by the other methods

observations on the tanh coth expansion method for finding solutions to nonlinear evolution equations abstract the tanh coth expansion method for finding solitary travelling wave solutions to nonlinear evolution equations has been used extensively in the literature it is a natural extension to the basic tanh function expansion method which was developed in the 1990s it usually delivers three types of solution namely a tanh function expansion a coth function expansion and a tanh coth expansion it is known that for every tanh function expansion solution there is a corresponding coth function expansion solution it is shown that there is a tanh coth expansion solution that is merely a disguised version of the coth solution in many papers such tanh coth solutions are erroneously claimed to be new however other tanh coth solutions may be delivered that are genuinely new in the sense that they would not be delivered via the basic tanh function method similar remarks apply to tan cot and tan cot expansion solutions

homotopy perturbation technique abstract the homotopy perturbation technique does not depend upon a small parameter in the equation by the homotopy technique in topology a homotopy is constructed with an imbedding parameter p 0 1 which is considered as a small parameter some examples are given the approximations obtained by the proposed method are uniformly valid not only for small parameters but also for very large parameters

quasi exact solutions of nonlinear differential equations abstract the concept of quasi exact solutions of nonlinear differential equations is introduced quasi exact solution expands the idea of exact solution for additional values of parameters of differential equation these solutions are approximate ones of nonlinear differential equations but they are close to exact solutions quasi exact solutions of the the kuramoto sivashinsky the korteweg de vries burgers and the kawahara equations are founded

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

simultaneous equations and panel data abstract this paper considers a simultaneous equations model with panel data and unobservable individual effects in each structural equation the effects may be fixed or random in the fixed effects case a conditional likehood approach leads to the within transformation just as in the single equation setting in the random effects case we allow an arbitrary number of the exogenous variables to be correlated with the effects and provide efficient gmm estimators along the lines of two stage and three stage least squares the case of different instruments in different equations is also considered

simultaneous equations with error components abstract in this paper we derive a limited as well as a full information estimator for the structural parameters of a simultaneous equations model with error components under this model the gain in efficiency by performing these estimators rather than the classical two stage and three stage least squares procedures is demonstrated it is shown that the full information estimator will reduce to the limited information estimator when the disturbances of different structural equations are uncorrelated with each other but not necessarily when all structural equations are just identified this is different from the analogous situation in the classical case

the effect of perturbed advection on a class of solutions of a non linear reaction diffusion equation in this work the traveling wave solutions of a one dimensional reaction diffusion equation with advection are studied the traveling wave solutions are obtained using the g g expansion method the shock thickness and spectral stability have been discussed for the obtained solution in the parameter interval the essential spectra of the perturbed and linearized differential operator about the traveling antikink and kink solutions at the equilibrium states are obtained the point spectrum is calculated using evans function with lie midpoint method and magnus method it is shown that for a symmetric potential well the traveling kink and antikink solutions which connect the stable equilibrium states of the system are stable it is observed that the perturbation on the advection exhibits contrasting effect on the solution properties shock thickness and the eigenvalue of kink and antikink solutions variation of the reaction coefficient leads to instability of the solutions unlike the diffusion coefficient which enhances the stability on the other hand the variation of reaction and diffusion coefficients show the monotonic effect on the shock thickness of the traveling kink and antikink solutions this study is expected to be useful in analyzing the slow or fast invasion and stability of the population movement in different steady states

a novel traveling wave solution for ostrovsky equation using exp function method in this paper we predict a new traveling wave solution of ostrovsky equation by using he s exp function method the method is straightforward and concise and its application shows an imminent prospective for the nonlinear problems in mathematical physics

extended simplest equation method for nonlinear differential equations abstract the modified simplest equation method to look for the exact solutions of the nonlinear differential equations is presented our approach is applied to search for the exact solutions of the sharma tasso olver and the burgers huxley equations the new exact solutions of these equations are obtained

a travelling wave solution to the ostrovsky equation in this paper we consider a nonlinear evolution equation like ostrovsky equation by using the hyperbolic tangent method and an exponential function approach a travelling wave solution for the ostrovsky equation is presented it is observed that both methods lead to the same type of solution

new traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized big frac g prime g big expansion method in this paper we construct new traveling wave solutions of some nonlinear evolution equations in mathematical physics via the 3 1 dimensional potential ytsf equation the 3 1 dimensional modified kdv zakharov kuznetsev equation the 3 1 dimensional kadomtsev petviashvili equation and the 1 1 dimensional kdv equation by using a generalized expansion method where g g satisfies the jacobi elliptic equation g 2 p g here we assume that p g is a polynomial of fourth order many new exact solutions in terms of the jacobi elliptic functions are obtained

a note on new travelling wave solutions to the ostrovsky equation in a recent paper by yasar e yasar new travelling wave solutions to the ostro vsky equation appl math comput 216 2010 3191 3194 new travelling wave solutions to the transformed reduced ostrovsky equation are presented in this note it is shown that some of these solutions are disguised versions of known solutions

special singularity function for continuous part of the spectral data in the associated eigenvalue problem for nonlinear equations the procedure for finding the solutions of the vakhnenko parkes equation by means of the inverse scattering method is described the continuous spectrum is taken into account in the associated eigenvalue problem the suggested special form of the singularity function for continuous part of the spectral data gives rise to the multi mode solutions the sufficient conditions are proved in order that these solutions become real functions the interaction of the n periodic waves is studied the procedure is illustrated by considering a number of examples

estimating multi way error components models with unbalanced data structures abstract i develop simple matrix algebra techniques that simplify and unify much of the previous literature on estimating error components models ecms in fact the simple analytic results provided here are useful for analyzing a very broad set of models with complex error structures to illustrate the techniques i develop the algebra for three and four way ecms explicitly in addition i provide monte carlo simulation evidence on the performance of several estimators for the three way ecm and estimate the model using data from a retail market where the three dimensions of data variation are products selling in many locations over time

a note on new kink shaped solutions and periodic wave solutions for the 2 1 dimensional sine gordon equation exact solutions of the nizhnik novikov veselov equation by li new kink shaped solutions and periodic wave solutions for the 2 1 dimensional sine gordon equation appl math comput 215 2009 3777 3781 are analyzed we have observed that fourteen solutions by li from 30 do not satisfy the equation the other 16 exact solutions by li can be found from the general solutions of the well known solution of the equation for the weierstrass elliptic function

new application of the g g expansion method to higher order nonlinear equations in this paper we extend the g g expansion method to higher order nonlinear equations as a result a series of new travelling wave solutions of the modified kawahara equation and the fifth order kdv equation have been obtained the travelling wave solutions are expressed by the hyperbolic functions the trigonometric functions and the rational functions it is shown that the g g expansion method presents a wider applicability for handling nonlinear evolution equations

variational iteration method some recent results and new interpretations this paper is an elementary introduction to the concepts of variational iteration method first the main concepts in variational iteration method such as general lagrange multiplier restricted variation correction functional are explained heuristically subsequently the solution procedure is systematically addressed in particular for nonlinear oscillators particular attention is paid throughout the paper to give an intuitive grasp for the method the main motivation is to put things together in a convenient form for later reference and systematic use

solitary solutions periodic solutions and compacton like solutions using the exp function method in this paper the exp function method is used for seeking solitary solutions periodic solutions and compacton like solutions of nonlinear differential equations the combined kdv mkdv equation and the liouville equation are chosen to illustrate the effectiveness and convenience of the proposed method

nonlinear differential equations of the second third and fourth order with exact solutions abstract we present the class of nonlinear ordinary differential equations of the second third and fourth order in a polynomial form with exact solutions this class has exact solutions in the form of solitary waves kinks and one periodic solutions

the g g expansion method and travelling wave solutions for a higher order nonlinear schrodinger equation abstract the higher order nonlinear schrodinger equation is reduced to a nonlinear ordinary differential equation ode by using a simple transformation various solutions of the nonlinear ode are obtained by the g g expansion method proposed recently with the aid of solutions of the nonlinear ode more explicit travelling wave solutions involving two arbitrary parameters of the higher order nonlinear schrodinger equation are found out the travelling waves are expressed by the hyperbolic functions trigonometric functions and rational functions when the parameters are taken as special values the solitary waves are also derived from the travelling waves

panel data and unobservable individual effects abstract an important purpose in pooling time series and cross section data is to control for individual specific unobservable effects which may be correlated with other explanatory variables e g latent ability in measuring returns to schooling in earnings equations or managerial ability in measuring returns to scale in firm cost functions using instrumental variables and the time invariant characteristics of the latent variable we derive 1 1 a test for the presence of this effect and for the over identifying restriction we use 2 2 necessary and sufficient conditions for identification of all the parameters in the model and 3 3 the asymptotically efficient instrumental variables estimator and conditions under which it differs from the within groups estimator we calculate efficient estimates of a wage equation from the michigan income dynamics data which indicate substantial differences from within groups and balestra nerlove estimates particularly a significantly higher estimate of the returns to schooling

a generalized g g expansion method and its application to the 2 1 dimensional broer kaup equations abstract in this paper a generalized g g expansion method is used to seek more general exact solutions of the 2 1 dimensional broer kaup equations as a result non travelling wave solutions with three arbitrary functions are obtained including hyperbolic function solutions trigonometric function solutions and rational solutions the proposed method is more powerful than wang et al s method in m l wang x z li j l zhang the g g expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics phys lett a 372 2008 417 423 and it can be used for many other nonlinear evolution equations in mathematical physics

letter to the editor a note on new exact solutions for the kawahara equation using exp function method exact solutions of the kawahara equation by assas l m b assas new exact solutions for the kawahara equation using exp function method j comput appl math 233 2009 97 102 are analyzed it is shown that all solutions do not satisfy the kawahara equation and consequently all nontrivial solutions by assas are wrong

exact solutions of the equation for surface waves in a convecting fluid abstract a method for finding exact solutions and the first integrals is presented the basic idea of the method is to use the value of the fuchs index that appears in the painleve test to construct the auxiliary equation for finding the first integrals and exact solutions of nonlinear differential equations it allows us to obtain the first integrals and new exact solutions of some nonlinear ordinary differential equations the main feature of the method is that we do not assign a solution function at the beginning we find this function during calculations this approach is conceptually equivalent to the third step of the painleve test and sometimes allows us to change this step our approach generalizes a number of other methods for finding exact solutions of nonlinear differential equations we demonstrate a method for finding the traveling wave solutions and the first integrals of the well known nonlinear evolution equation for description of surface waves in a convecting liquid the general solution of this equation at some conditions on parameters and new traveling wave solutions of the fourth order equation are found

on solutions of generalized modified korteweg de vries equation of the fifth order with dissipation the generalized modified korteweg de vries equation of the fifth order with dissipation is considered the painleve test is applied for studying integrability of this equation it is shown that the generalized modified korteweg de vries equation of the fifth order does not pass the painleve test in the general case but has the expansion of the solution in the laurent series as a consequence the equation can have some exact solutions at additional conditions on the parameters of the equation we present the effective modification of methods for finding of solitary wave and elliptic solutions of nonlinear differential equations solitary wave and elliptic solutions of the generalized modified korteweg de vries equation of the fifth order are found by means of expansion for solution in the laurent series these solutions can be used for description of nonlinear waves in the medium with dissipation dispersion

extend three wave method for the 1 2 dimensional ito equation abstract in this work extend three wave method etm is used to construct the novel multi wave solutions of the 1 2 dimensional ito equation as a result three soliton solution doubly periodic solitary wave solutions periodic two solitary wave solutions are obtained it is shown that the extend three wave method may provide us with a straightforward and effective mathematical tool for seeking multi wave solutions of higher dimensional nonlinear evolution equations

new exact homoclinic wave and periodic wave solutions for the ginzburg landau equation abstract new exact solutions including homoclinic wave and periodic wave solutions for the 2d ginzburg landau equation are obtained using the auxiliary function method and the g g expansion method respectively the solutions are expressed by the hyperbolic functions and the trigonometric functions there result shows that there exists a kink wave solution which tends to one and the same periodic wave solution as time tends to infinite

travelling wave solutions to the two dimensional kdv burgers equation travelling wave solutions for the two dimensional kdv burgers equation are obtained by using mathematica they are shown to be sums of a shock wave and solitary wave

on the application of the exp function method to the kp equation for n soliton solutions abstract we observe that the form of the kadomstev petviashvili equation studied by yu 2011 s yu n soliton solutions of the kp equation by exp function method appl math comput 2011 doi 10 1016 j amc 2010 12 095 is incorrect we claim that the n soliton solutions obtained by means of the basic exp function method and some of its known generalizations do not satisfy the equation considered we emphasize that yu s results except only one cannot be solutions of the correct form of the kadomstev petviashvili equation in addition we provide some correct results using the same approach

a note on abundant new exact solutions for the 3 1 dimensional jimbo miwa equation abstract we demonstrate that eight from twenty seven solutions obtained by li and dai abundant new exact solutions for the 3 1 dimensional jimbo miwa equation j math anal appl 361 2010 587 590 are wrong and do not satisfy the equation the other nineteen exact solutions are not new solutions and can be found from the well known solution

exact solitary waves in a convecting fluid the perturbed korteweg de vries equation ut lambda 1uux lambda 2uxxx lambda 3uxxxx lambda 4 uux x lambda 5uxx 0 which describes the evolution of long shallow waves in a convecting fluid when the critical rayleigh number slightly exceeds its critical value admits two types of exact solitary wave solution

exact traveling solutions of some nonlinear evolution equation by g g expansion method in this paper we establish exact solutions for some nonlinear evolution equations the g g expansion method was used to construct traveling wave solutions of ramani s equations in this method we take the advantages of the general solutions of the second order lode to solve effectively many nonlinear evolution equations the g g expansion method presents a wider applicability for handling nonlinear wave equations

painleve analysis and exact solutions for the modified korteweg de vries equation with polynomial source the modified korteweg de vries equation with polynomial source is considered using the painleve test we show that the generalized korteweg de vries equation is not integrable by the inverse scattering transform however there are some expansions of solution in the laurent series and some exact solutions can exist some traveling wave solutions of the modified korteweg de vries equation with polynomial source are found

polynomials in logistic function and solitary waves of nonlinear differential equations properties of polynomials in logistic function are studied it is demonstrated that these polynomials can be used for construction of exact solutions to nonlinear differential equations nonlinear differential equations with exact solutions in the form of polynomials in logistic function are found it is shown there are solitary waves of nonlinear differential equations described by polynomial in logistic function with many maximum and minimum

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

exact travelling solutions for the lax s seventh order kdv equation by sech method and rational exp function method in this paper we establish exact solutions for a nonlinear evolution equation the sech method and the exp function method are used to construct the solitary travelling wave solutions of lax s seventh order kdv equation these solutions may be important of significance for the explanation of some practical physical problem

analytic study on two nonlinear evolution equations by using the g g expansion method abstract the validity and reliability of the so called g g expansion method is tested by applying it to two nonlinear evolutionary equations solutions in more general forms are obtained when the parameters are taken as special values it is observed that the previously known solutions can be recovered new rational function solutions are also presented being concise and less restrictive the method can be applied to many nonlinear partial differential equations

kink solitary solutions to generalized riccati equations with polynomial coefficients abstract inverse and direct balancing methods for the construction of kink solitary solutions to generalized riccati equations with polynomial coefficients are presented in this paper necessary and sufficient conditions for the existence of kink solitary solutions are derived in terms of the equation s parameters and initial conditions the proposed technique enables a straightforward derivation of parameters of solitary solutions computational experiments are used to demonstrate the efficiency of the proposed analytical approach