the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

generalized multiple riccati equations rational expansion method with symbolic computation to construct exact complexiton solutions of nonlinear partial differential equations in this paper based on symbolic computation and the idea of rational expansion method a generalized multiple riccati equations rational expansion method gmrere is proposed to uniformly construct a series of exact complexiton solutions for nonlinear partial differential equations compared with most existing tanh function methods and rational expansion methods the proposed method not only recovers some known solutions but also finds some new and general complexiton solutions the efficiency of the method can be demonstrated on 2 1 dimensional burgers equation

homotopy perturbation method for fractional kdv equation in this paper the homotopy perturbation method is directly applied to derive approximate solutions of the fractional kdv equation the results reveal that the proposed method is very effective and simple for solving approximate solutions of fractional differential equations

hamiltonian structure and integrability of the stationary kuramoto sivashinsky equation in this article the stationary kuramoto sivashinsky ks equation is studied it is shown first that this equation can be transformed into a one dimensional hamiltonian system describing the motion of a particle in a time dependent potential second working with this formalism and coming back then to the initial ks equation a subset of initial conditions is derived for which the corresponding solutions u x will behave like the dominant pole 120 x x0 3 deduced from the painleve analysis and will explode in a finite time finally special attention is given to the well known kuramoto tsuzuki solution and it is shown that provided the independent variable x is initialized in a specified domain this solution explodes also like 120 x x0 3

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

triviality of the prolongation algebra of the kuramoto sivashinsky equation the authors apply the well known wahlquist estabrook prolongation technique to the kuramoto sivashinsky equation the prolongation algebra turns out to be trivial in the sense that it is commutative this supports nonintegrability of the equation

construction of non travelling wave solutions for the generalized variable coefficient gardner equation with the aid of two first order nonlinear ordinary differential equations the new generalized algebraic method is used to study the generalized variable coefficient gardner equation the main idea of the method is to take full advantage of solutions to the first order ordinary differential equations more new exact non travelling solutions which include soliton solutions combined soliton solutions triangular periodic solutions jacobi elliptic function solutions and combined jacobi elliptic function solutions for the gardner equation are obtained the method used here can be also extended to many other nonlinear partial differential equations

linearity inside nonlinearity exact solutions to the complex ginzburg landau equation abstract systems of two linear partial differential equations pdes with constant coefficients define a natural basis of elementary functions to build some exact solutions to nonlinear pdes for the one dimensional complex ginzburg landau equation the usual representations of the complex field re a or a are multivalued which makes difficult the search for exact solutions in this manner fortunately the painleve analysis naturally introduces an elementary single valued like representation of a by two fields z grad respectively complex abd real uniquely defined by an explicit expression for and a ze i another important feature is the invariance by parity on a which increases the class of expected solutions this allows to retrieve quite easily the four famous solutions of nozaki and bekki represented by the constant coefficients of two linear partial differential equations and a finite set of constants

travelling wave solutions for the generalized zakharov kuznetsov equation with higher order nonlinear terms abstract with the aid of symbolic computation and two auxiliary ordinary differential equations the new generalized algebraic method is extended to the generalized zakharov kuznetsov gzk equation with higher order nonlinear terms for constructing a series of new and more general travelling wave solutions because of the higher order nonlinear terms the equation can not be directly dealt with by the method and require some kinds of techniques by means of two proper transformations we transform the gzk equation to an ordinary differential equation that is easy to solve and find a rich variety of new exact travelling wave solutions for the gzk equation which include soliton solutions combined soliton solutions triangular periodic solutions jacobi elliptic function solutions combined jacobi elliptic function solutions and rational function solutions the method used here can be also extended to other nonlinear partial differential equations with higher order nonlinear terms

exact solutions of the multidimensional derivative nonlinear schrodinger equation for many body systems of criticality the authors investigate the problem of strongly interacting many body systems near criticality as recently described in terms of nonlinear dynamics by dixon and tuszynski 1989 they show that in the first order of approximation the equation of motion for the order parameter can be mapped on the derivative nonlinear schrodinger equation and thus can be solved exactly they solve the equations both in the absence and presence of current densities

the quantum group suq 2 and a q analogue of the boson operators a new realisation of the quantum group suq 2 is constructed by means of a q analogue to the jordan schwinger mapping determining thereby both the complete representation structure and q analogues to the wigner and racah operators to achieve this realisation a new elementary object is defined a q analogue to the harmonic oscillator the uncertainty relation for position and momentum in a q harmonic oscillator is quite unusual

link between solitary waves and projective riccati equations many solitary wave solutions of nonlinear partial differential equations can be written as a polynomial in two elementary functions which satisfy a projective hence linearizable riccati system from that property the authors deduce a method for building these solutions by determining only a finite number of coefficients this method is much shorter and obtains more solutions than the one which consists of summing a perturbation series built from exponential solutions of the linearized equation they handle several examples for the henon heiles hamiltonian system they obtain several exact solutions one of them defines a new solitary wave solution for a coupled system of boussinesq and nonlinear schrodinger equations for a third order dispersive equation with two monomial nonlinearities they isolate all cases where the general solution is single valued

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

solutions of a 2 1 dimensional dispersive long wave equation a special type of multisoliton solution with a particular dispersion relation is obtained for wu zhang equation which describes 2 1 dimensional dispersive long waves by the standard weiss tabor carnvale painleve truncation expansion using a nonstandard truncation of a modified conte s invariant painleve expansion two different types of soliton solutions without any dispersive relation is found two types of periodic wave solutions expressed by jacobi elliptic functions are found by the truncations of a special extended painleve expansion the soliton solutions are special cases of the corresponding periodic solutions

approximate solution for system of differential difference equations by means of the homotopy analysis method abstract in this paper the homotopy analysis method is successfully applied to solve approximate solutions of the differential difference system the solution of another relativistic toda lattice system is considered comparisons made between the results of the proposed method and exact solutions reveal that the homotopy analysis method is very effective in solving differential difference system

lipschitz equivalence of cantor sets and algebraic properties of contraction ratios in this paper we investigate the lipschitz equivalence of dust like self similar sets in rd one of the fundamental results by falconer and marsh on the lipschitz equivalence of cantor sets mathematika 39 1992 223 233 establishes conditions for lipschitz equivalence based on the algebraic properties of the contraction ratios of the self similar sets in this paper we extend the study by examining deeper such connections a key ingredient of our study is the introduction of a new equivalent relation between two dust like self similar sets called matchable condition thanks to a certain measure preserving property of bi lipschitz maps between dust like self similar sets we show that the matchable condition is a necessary condition for lipschitz equivalence using the matchable condition we prove several conditions on the lipschitz equivalence of dust like self similar sets based on the algebraic properties of the contraction ratios which include a complete characterization of lipschitz equivalence when the multiplication groups generated by the contraction ratios have full rank we also completely characterize the lipschitz equivalence of dust like self similar sets with two branches i e they are generated by ifs with two contractive similarities some other results are also presented including a complete characterization of lipschitz equivalence when one of the self similar sets has uniform contraction ratio

a new coupled sub equations expansion method and novel complexiton solutions of 2 1 dimensional burgers equation in this paper based on symbolic computation and the idea of rational expansion method a new coupled sub equations method is devised to uniformly construct a series of exact complexiton solutions for nonlinear evolution equations compared with most existing tanh function methods and other sophisticated methods the proposed method not only recover some known solutions but also find some new and general solutions which include many new types of complexiton solutions the efficiency of the method can be demonstrated on 2 1 dimensional burgers equation

traveling wave solutions of the generalized nonlinear evolution equations solitary wave solutions for a family of nonlinear evolution equations with an arbitrary parameter in the exponents are constructed some of the obtained solutions seem to be new

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

painleve analysis and backlund transformation in the kuramoto sivashinsky equation the authors apply the painleve test to the kuramoto sivashinsky nonlinear partial differential equation which describes many interesting fluid motions the equation passes the test in a weak sense although the painleve analysis does not yield the general solution they perform the backlund transformation in order to obtain new particular solutions the authors find explicitly all the solutions of the set of equations which define the painleve backlund transformation they reduce to only one type namely the already known kink shaped solitary wave

gap sequences of fractal squares abstract we discuss gap sequences of a class of fractal squares which have nontrivial connected components at most in one direction

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

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

exact solutions of the complex modified korteweg de vries equation firstly some similarity reductions of the complex modified korteweg de vries equation cmkdv which arises in the asymptotic interpretation of one dimensional plane wave propagation in a quadratic micropolar medium are discussed although it is not a soliton equation solvable by inverse scattering transformation its similarity reductions obtained by the use of lie group methods are of mathematical interest secondly the painleve analysis developed by weiss et al 1983 for nonlinear partial differential equations is applied to the cmkdv equation and the data obtained by the truncation technique yield some analytical solutions of the ordinary modified korteweg de vries equation and travelling wave solutions of the cmkdv equation which are also solutions of the similarity reduction obtained by classical lie group analysis

the painleve property for partial differential equations ii backlund transformation lax pairs and the schwarzian derivative in this paper we investigate the painleve property for partial differential equations by application to several well known partial differential equations burgers kdv mkdv bousinesq higher order kdv and kp equations it is shown that consideration of the singular manifold leads to a formulation of these equations in terms of the schwarzian derivative this formulation is invariant under the moebius group acting on dependent variables and is shown to obtain the appropriate lax pair linearization for the underlying nonlinear pde

a note on the progressive wave solution of the perturbed korteweg devries equation with variable dissipation in this note utilizing the method presented in engelbrecht 1991 and demiray 2002 we have studied the propagation of progressive waves in perturbed kdv equation with variable dissipation coefficient the cases of constant and variable dissipation coefficient are studied separately and the results are compared with each other it is seen that for both cases the amplitude and wave speed decrease with increasing time

path integrals for quantum algebras and the classical limit coherent states path integral formalism for the simplest quantum algebras q oscillator suq 2 and suq 1 1 is introduced in the classical limit canonical structure is derived with a modified symplectic and riemannian metric non constant deformation induced curvature for the phase spaces is obtained

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

modified simple equation method for nonlinear evolution equations abstract this paper reflects the implementation of a reliable technique which is called modified simple equation method msem for solving evolution equations the proposed algorithm has been successfully tested on two very important evolution equations namely fitzhugh nagumo equation and sharma tasso olver equation numerical results are very encouraging

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

the riemann zeta function and the one dimensional weyl berry conjecture for fractal drums based on his earlier work on the vibrations of drums with fractal boundary the first author has refined m v berry s conjecture that extended from the smooth to the fractal case h weyl s conjecture for the asymptotics of the eigenvalues of the laplacian on a bounded open subset of w see 16 we solve here in the one dimensional case that is when n 1 this modified weyl berry conjecture we discover in the process some unexpected and intriguing connections between spectral geometry fractal geometry and the riemann zeta function we therefore show that one can hear that is recover from the spectrum not only the minkowski fractal dimension of the boundary as was established previously by the first author but also under the stronger assumptions of the conjecture its minkowski content a fractal analogue of its length we also prove still in dimension one a related conjecture of the first author as well as its converse which characterizes the situation when the error estimates of the aforementioned paper are sharp

analytic solutions of a microstructure pde and the kdv and kadomtsev petviashvili equations by invariant painleve analysis and generalized hirota techniques abstract truncated painleve expansions invariant painleve analysis and generalized hirota expansions are employed in combination to solve partially reduce to quadrature the integrable kdv and kp equations and a nonintegrable generalized microstructure gms equation although the multisolitons of the kdv and kp equations are very well known the solutions obtained here for all the three nlpdes are novel and non trivial the solutions obtained via invariant painleve analysis are all complicated rational functions with arguments which themselves are confluent hypergeometric kdv or trigonometric gms functions of various distinct non traveling kdv and traveling wave variables in some cases this is slightly reminiscent of doubly periodic elliptic function solutions when nonlinear ode systems are reduced to quadratures the solutions obtained by the use of recently generalized hirota type expansions in the truncated painleve expansions are closer in functional form to conventional hyperbolic secant solutions although with non trivial traveling wave arguments which are distinct for the three nlpdes considered here

on the behavior of solutions of a class of nonlinear partial differential equations the behavior of the steady state or the traveling wave solutions for a class of nonlinear partial differential equations is studied the nonlinearity in these equations is expressed by the presence of the convective term it is shown that the steady state or the traveling wave solution may explode at a finite value of the spatial or the characteristic variable this holds whatever the order of the spatial derivative term in these equations furthermore new special solutions of a set of equations in this class are also found

numerical solutions for fractional kdv burgers equation by adomian decomposition method abstract based on the symbolic computation system maple adomian decomposition method developed for differential equations of integer order is directly extended to derive explicit and numerical solutions of the fractional kdv burgers equation the fractional derivatives are described in the caputo sense according to my knowledge this paper represents the first available numerical solutions of the nonlinear fractional kdv burgers equation with time and space fractional derivatives finally the solutions of our model equation are calculated in the form of convergent series with easily computable components

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

the construction of the q analogues of the harmonic oscillator operators from ordinary oscillator operators the q analogues of boson operators are constructed from ordinary boson operators by an embedding approach accordingly the q deformed quantum algebras su n q can be obtained straightforwardly from corresponding universal enveloping algebras of lie algebra su n

elliptic solutions for a family of fifth order nonlinear evolution equations abstract the family of fifth order nonlinear evolution equations is studied some traveling wave elliptic solutions are found the classification of these exact solutions is given

a new variable coefficient korteweg de vries equation based sub equation method and its application to the 3 1 dimensional potential ytsf equation with the aid of maple we present variable coefficient korteweg de vries equation based sub equation method the key idea of our method is to take advantage of the variable coefficient korteweg de vries equation and its various solutions to generate various solutions of nonlinear evolution equations the efficiency of the method can be demonstrated on the 3 1 dimensional potential ytsf equation and we construct successfully its new styles of solutions

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

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

on the q oscillator and the quantum algebra suq 1 1 the authors discuss some problems of the q deformed harmonic oscillator different q bosonisations of the quantum suq 1 1 algebra are given and the corresponding infinite dimensional representations of discrete series are analysed

from singular manifold equations to integrable evolution equations the singular manifold equations are used to construct nonlinear integrable partial differential equations a number of well known integrable equations hierarchies of korteveg de vries caudrey dodd gibbon kaup kuperschmidt and harry dym are obtained some new integrable equations are presented a possible approach to classification of integrable evolution equations is discussed

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

painleve analysis rational and special solutions of variable coefficient korteweg de vries equations painleve analysis of two variable coefficient korteweg de vries equations are considered the painleve test for these equations is applied the condition for the painleve property of the equations are found some rational and special solutions are presented

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

complex analytic realizations for quantum algebras a method for obtaining complex analytic realizations for a class of deformed algebras based on their respective deformation mappings and their ordinary coherent states is introduced explicit results of such realizations are provided for the cases of the q oscillators q weyl heisenberg algebra and for the suq 2 and suq 1 1 algebras and their coproducts they are given in terms of a series in powers of ordinary derivative operators which act on the bargmann hilbert space of functions endowed with the usual integration measures in the q 1 limit these realizations reduce to the usual analytic bargmann realizations for the three algebras

application of the extended homotopy perturbation method to a kind of nonlinear evolution equations based on the homotopy perturbation method we propose a new extended homotopy perturbation method we apply the method to solve a kind of nonlinear evolution equations with the help of the symbolic computation system maple the success of the paper lies on the fact that we do not conform to the traditional homotopy mode but construct a new homotopy of the given equations the results reveal that we can obtain the approximation solution of a kind of nonlinear evolution equations

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

elementary particles as solutions of the sivashinsky equation abstract stationary spherically symmetric solutions of the sivashinsky equation 1 c 2 s 2 t s 2 m 2 c 2 s 3 m 2 c 2 2 s are looked for the problem is reduced to finding all admissible solutions y y r of the ode d 2 dr 2 2 r d dr 1 d dr 2 r y y 2 i e solutions which are defined on the half line 0 r and satisfy y 0 y 0 it is proved that for each y 0 0 34 0 33 the solution of the initial value problem with y 0 y 0 0 is admissible in terms of the action function s these solutions are interpreted as free relativistic particles the proof of the result employs analytic asymptotic expansion near r 0 and r and a new technique of rigorous estimates by a computer the proved interval of existence y 0 0 34 0 33 nearly coincides with the one obtained by numerical experiments

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

lipschitz equivalence of self similar sets and hyperbolic boundaries abstract kaimanovich 2003 9 introduced the concept of augmented tree on the symbolic space of a self similar set it is hyperbolic in the sense of gromov and it was shown by lau and wang 2009 12 that under the open set condition a self similar set can be identified with the hyperbolic boundary of the tree in the paper we investigate in detail a class of simple augmented trees and the lipschitz equivalence of such trees the main purpose is to use this to study the lipschitz equivalence problem of the totally disconnected self similar sets which has been undergoing some extensive development recently

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