group classification of variable coefficient generalized kawahara equations an exhaustive group classification of variable coefficient generalized kawahara equations is carried out as a result we derive new variable coefficient nonlinear models admitting lie symmetry extensions all inequivalent lie reductions of these equations to ordinary differential equations are performed we also present some examples on the construction of exact and numerical solutions

on the stability of dense point spectrum for self adjoint operators let a be a random self adjoint operator with fixed orthonormal eigenvectors but with independently distributed random eigenvalues typically for the eigenvalue distributions a is considered to have a dense point spectrum almost surely a s a class of perturbations b is exhibited such that a b has only point spectrum a s examples are also constructed including a rank one perturbation b such that a b has no eigenvalues for 0 a s despite a having dense point spectrum a s

the modified extended tanh function method for solving burgers type equations abstract by means of the modified extended tanh function metf method the multiple travelling wave solutions of some different kinds of nonlinear partial differential equations are presented and implemented in a computer algebraic system solutions for the nonlinear equations such as one dimensional burgers kdv burgers coupled burgers and two dimensional burgers equations are obtained precisely and so the efficiency of the method can be demonstrated

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

fixed point theorems for set valued maps and existence principles for integral inclusions new fixed point theorems of monch type are presented for set valued maps these theorems are then used to establish general existence principles for hammerstein integral inclusions in banach spaces

new exact travelling wave solutions of kawahara type equations abstract the auxiliary equation method is used to find analytic solutions for the kawahara and modified kawahara equations it is well known that different types of exact solutions of the given auxiliary equation produce new types of exact travelling wave solutions to nonlinear equations in this paper new exact solutions of the auxiliary equation are presented using these solutions many new exact travelling wave solutions for the kawahara type equations are obtained

positive lyapunov exponents for schrodinger operators with quasi periodic potentials we present a new simple way to estimate the rate of exponential growth lyapunov exponent of solutions of the finite difference schrodinger equation h e psi n mathop limits def psi n 1 psi n 1 lambda f alpha n theta psi n heref is a non constant real analytic function of period 1 and is irrational for large we prove that the lyapunov exponent is positive for every energye in the spectrum ofh and a e in particular the absolutely continuous spectrum ofh is empty in the continuum we study the quasi periodic operator onl2 r h frac d 2 dx 2 k 2 cos x cos alpha x theta for largek and show that for wide intervals of low energies the lyapunov exponent is positive the main idea which originated from m herman s subharmonic argument 11 is to deform the phase to the complex plane this enables us to avoid small denominator problems by moving them off the axis making estimates much easier to perform we recover the information for real using an elementary extension of jensen s formula subharmonicity

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

pure point spectrum for discrete almost periodic schrodinger operators the finite difference schrodinger operator on m is considered hu j left sum limits v 1 m d v 2 right u j frac 1 varepsilon q j u j u in ell 2 mathbb z m where sum limits v 1 m d v 2 is the difference laplacian inm dimensions for sufficiently small almost periodic potentialsq j are constructed such that the operatorh has only pure point spectrum the method is an inverse spectral procedure which is a modification of the kolmogorov arnol d moser technique

remark on exp function method for the exact solutions of fifth order kdv equation and modified burgers equation appl math comput 2009 doi 10 1016 j amc 2009 07 009 abstract by means of the exp function method inan and ugurlu appl math comput 2009 doi 10 1016 j amc 2009 07 009 reported eight expressions for being solutions to the two equations studied in fact all of them can be easily simplified to constants

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

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

a fourth order numerical scheme for solving the modified burgers equation a finite difference scheme based on fourth order rational approximants to the matrix exponential term in a two time level recurrence relation is proposed for the numerical solution of the modified burgers equation the resulting nonlinear system which is analyzed for stability is solved using an already known modified predictor corrector scheme the results arising from the experiments are compared with the corresponding ones known from the available literature

the classification of rokhlin flows on mathrm c c algebras we study flows on mathrm c algebras with the rokhlin property we show that every kirchberg algebra carries a unique rokhlin flow up to cocycle conjugacy which confirms a long standing conjecture of kishimoto we moreover present a classification theory for rokhlin flows on mathrm c algebras satisfying certain technical properties which hold for many mathrm c algebras covered by the elliott program as a consequence we obtain the following further classification theorems for rokhlin flows firstly we extend the statement of kishimoto s conjecture to the non simple case up to cocycle conjugacy a rokhlin flow on a separable nuclear mathcal o infty absorbing mathrm c algebra is uniquely determined by its induced action on the prime ideal space secondly we give a complete classification of rokhlin flows on simple classifiable kk contractible mathrm c algebras two rokhlin flows on such a mathrm c algebra are cocycle conjugate if and only if their induced actions on the cone of lower semicontinuous traces are affinely conjugate

harmonic analysis approach to gromov hausdorff convergence for noncommutative tori we show that the rotation algebras are limits of matrix algebras in a very strong sense of convergence for algebras with additional lipschitz structure our results generalize to higher dimensional noncommutative tori and operator valued coefficients in contrast to previous results by rieffel li kerr and latremoliere we use lipschitz norms induced by the carre du champ of certain natural dynamical systems including the heat semigroup

variational iteration method for solving burger s and coupled burger s equations by means of variational iteration method the solutions of burger s equation and coupled burger s equations are exactly obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

norm estimates of almost mathieu operators abstract we estimate the norm of the almost mathieu operator h u u 2 v v regarded as an element in the rotation c algebra a c u v unitaries u v e 2 i v u in the process we prove for every r and 1 4 1 2 the inequality h 4 2 1 1 tan 1 1 cos 2 4 2 min 4 2 this significantly improves the inequality h 2 2 2 1 4 1 2 conjectured by beguin valette and zuk

wandering vectors for irrational rotation unitary systems abstraci an abstract characterization for those irrational rotation unitary systems with complete wandering subspaces is given we prove that an irrational rotation unitary system has a complete wandering vector if and only if the von neumann algebra generated by the unitary system is finite and shares a cyclic vector with its commutant we solve a factorization problem of dai and larson negatively for wandering vector multipliers and strengthelsl this by showing that for an irrational rotation unitary system u every unitary operator in w u is a wandering vector multiplier moreover we show that there is a class of wandering vector rilultipliers induced in a natural way by pairs of characters of the integer group 2 which fail to factor even as the product of a unitary in u and a unitary in w u incomplete maximal wandering subspaces are also considered and some questions are raised

the rotation number for almost periodic potentials we define and analyze the rotation number for the almost periodic schrodinger operatorl d2 dx2 q x we use the rotation number to discuss i the spectrum ofl ii its relation to the korteweg de vries equation

on series expansions giving closed form solutions of korteweg de vries like equations korteweg devries kdv like equations with higher degree nonlinearity are solved by a direct algebraic technique due to hereman et al j phys a 19 1986 pp 607 628 for two kdv like equations one with fifth degree nonlinearity the other a combined kdv and mkdv equation for particular choices of the coefficients of the nonlinear terms the kink and antikink solutions found by dey are recovered furthermore soliton solutions of the combined kdv and mkdv equation are found for all values of the coefficients closed form solutions for the calogero degasperis fokas modified mkdv equation are also developed applications of the solutions of these equations in quantum field theory plasma physics and solid state physics are mentioned the hereman et al method is illustrated and slightly extended and this direct series method is briefly compared to hirota s method

examples of discrete schrodinger operators with pure point spectrum we present a general approach for constructing potentials for the discrete schrodinger equation of arbitrary dimension having only pure point spectrum we give examples of limit periodic potentials of that kind such that the pure point spectrum is dense in an interval or a cantor set of measure zero

solitary wave solutions of nonlinear evolution and wave equations using a direct method and macsyma the direct algebraic method for constructing travelling wave solutions on nonlinear evolution and wave equations has been generalized and systematized the class of solitary wave solutions is extended to analytic rather than rational functions of the real exponential solutions of the linearized equation expanding the solutions in an infinite series in these real exponentials an exact solution of the nonlinear pde is obtained whenever the series can be summed methods for solving the nonlinear recursion relation for the coefficients of the series and for summing the series in closed form are discussed the algorithm is now suited to solving nonlinear equations by any symbolic manipulation program this direct method is illustrated by constructing exact solutions of a generalized kdv equation the kuramoto sivashinski equation and a generalized fisher equation

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

almost periodic jacobi matrices associated with julia sets for polynomials let be the jacobi matrix associated with polynomialt z of degreen 2 the spectrum of is the julia set associated witht z which in many cases is a cantor set let 1 denote the result of omitting the first row and column ofj then it is shown that the spectrum of 1 may be purely discrete

franco american meeting on the mathematics of random and almost periodic potentials we present the abstracts of papers given at a conference held at the ecole polytechnique in june 1983 on the mathematics of random and almost periodic potentials

af embeddings of c t2 with a prescribed k theory let a be a unital af algebra without finite dimensional quotients our main result is the classification of the group homomorphisms k0 c t2 k0 a which are induced by unital star homomorphisms c t2 a specifically for some exactly when preserves the order unit and maps the reduced k theory of the torus into the kernel of for all bounded traces a c

choquet boundaries and efficiency this research paper is devoted to establish the coincidence between choquet boundaries and a new type of approximate efficient points sets in ordered hausdorff locally convex spaces being based on the first result established by us concerning such a property as this for pareto type efficient points sets and the corresponding choquet boundaries of non empty compact sets with respect to appropriate convex cones of real increasing and continuous functions thus the main result represents a strong connection between two great fields of mathematics the axiomatic theory of potential and vector optimization the present study contains also important relationships concerning strong optimization and approximate efficiency interesting examples pertinent remarks and some open problems

classification of outer actions of zn on o2 abstract we will show that any two outer actions of z n on o 2 are cocycle conjugate

domain wall solutions of kdv like equations with higher order nonlinearity the author considers certain nonlinear partial differential equations which are korteweg de vries kdv like equations with higher order nonlinearity it is shown that these have kink domain wall solutions for particular values of the coefficients of the nonlinear terms the solutions are compared with the standard known solution of the lambda phi 2n field theories some conservation laws for these systems of equations are also given

new exact solutions for the kawahara equation using exp function method in this paper we applied the exp function method to solve the kawahara equation this method can be used to obtain new exact solutions and periodic solutions with parameters are obtained it is shown that the exp function method with the help of symbolic computation provides a very effective and powerful mathematical tools for discrete nonlinear evolution equations in mathematical physics

spectral behavior of quasi periodic potentials spectral properties of schrodinger operators of the typeh v where is the laplacian v a quasiperiodic potential and a coupling constant are developed v is taken to be finite sum of exponentials with generic frequencies for small a strong stability is shown on the other hand examples in the finite diffeence case are given for which a transition in the type of spectrum occurs as is increased

multivalued fixed point theorems in terms of weak topology and measure of weak noncompactness abstract we present several fixed point theorems for multimaps in banach spaces which in turn are multivalued versions of the monch daher darbo and sadovskii theorems the main assumptions of our results are formulated in terms of weak topology and an axiomatic definition of measure of weak noncompactness our theorems extend in a broad sense some new and classical results moreover a sadovskii type theorem stated in 2011 is improved

gauss polynomials and the rotation algebra newton s binomial theorem is extended to an interesting noncommutative setting as follows if in a ring ba ab with commuting witha andb then the generalized binomial coefficient left begin array 20 c n k end array right r arising in the expansion left a b right n sum limits k 0 n left begin array 20 c n k end array right gamma a n k b k resulting from these relations is equal to the value at of the gaussian polynomial left begin array 20 c n k end array right frac left n right left k right left n k right where m 1 x m 1 x m 1 1 x this is of course known in the case 1 from this it is deduced that in the universal c algebraa gq generated by unitariesu andv such thatvu e 2 i uv the spectrum of the self adjoint element u v u v has all the gaps that have been predicted to exist provided that either is rational or is a liouville number in the latter case the gaps are labelled in the natural way viak theory by the set of all non zero integers and the spectrum is a cantor set

extending states on preordered semigroups and the existence of quasitraces on c algebras abstract it is shown that every state on a subsemigroup of a scaled preordered semigroup extends to the whole semigroup extending a theorem of goodearl and handelman as an application every state on k0 a for a unital c algebra a comes from a quasitrace

z2 actions on kirchberg algebras abstract we classify a large class of z 2 actions on the kirchberg algebras employing the kasparov group kk 1 as the space of classification invariants

classification of uniformly outer actions of z2 on uhf algebras we give a complete classification up to cocycle conjugacy of uniformly outer actions of on uhf algebras in particular it is shown that any two uniformly outer actions of on a uhf algebra of infinite type are cocycle conjugate we also classify them up to outer conjugacy

exp function method for the exact solutions of fifth order kdv equation and modified burgers equation abstract in this paper we implemented the exp function method for the exact solutions of the fifth order kdv equation and modified burgers equation by using this scheme we found some exact solutions of the above mentioned equations

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

anderson localization for time quasi periodic random schrodinger and wave equations we prove that at large disorder with large probability and for a corresponding set of diophantine frequencies of large measure anderson localization in d is stable under localized time quasi periodic perturbations by proving that the associated quasi energy operator has pure point spectrum the main tools are the frohlich spencer mechanism for the random component and the bourgain goldstein schlag mechanism for the quasi periodic component this paper paves the way for the construction of time quasi periodic kam type of solutions of non linear random schrodinger equations in bw

the quantum gromov hausdorff propinquity we introduce the quantum gromov hausdorff propinquity a new distance between quantum compact metric spaces which extends the gromovhausdorff distance to noncommutative geometry and strengthens rieffel s quantum gromov hausdorff distance and rieffel s proximity by making isomorphism a necessary condition for distance zero while being well adapted to leibniz seminorms this work offers a natural solution to the long standing problem of finding a framework for the development of a theory of leibniz lip norms over c algebras

how far one can go with the exp function method a criterion determining if an exact solution of a differential equation can be expressed in a form comprising a finite number of exponential functions is constructed in this paper this criterion is based on the concept of ranks of hankel matrixes constructed from sequences of coefficients produced by symbolic multiplicative operator techniques the employment of this criterion also gives an answer on the structure of the solution several examples are used to illustrate this concept

a metal insulator transition for the almost mathieu model we study the spectrum of the almost mathieu hamiltonian left h x psi right left n right psi left n 1 right psi left n 1 right 2 mu cos left x n theta right psi left n right n in mathbb z where is an irrational number andx is in the circle mathbb t for a small enough coupling constant and anyx there is a closed energy set of non zero measure in the absolutely continuous spectrum ofh for sufficiently high and almost allx we prove the existence of a set of eigenvalues whose closure has positive measure the two results are obtained for a subset of irrational numbers of full lebesgue measure

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

the numerical simulation for stiff systems of ordinary differential equations in this paper the variational iteration method is applied to solve systems of ordinary differential equations in both linear and nonlinear cases focusing interest on stiff problems some examples are given to illustrate the accuracy and effectiveness of the method we compare our results with results obtained by the adomian decomposition method this comparison reveals that the variational iteration method is easier to be implemented in fact the variational iteration method is a promising method to various systems of linear and nonlinear equations

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

comment on new exact solutions for the kawahara equation using exp function method j comput appl math 233 2009 97 102 assas laila m b assas new exact solutions for the kawahara equation using exp function method j comput appl math 233 2009 97 102 found some supposedly new exact solutions to the kawahara equation by means of the exp function method unfortunately they are incorrect we emphasize that the article contains erroneous formulas and resulting relations in fact no numerical method was used

n soliton solutions of the kp equation by exp function method abstract in this paper the exp function method is generalized to determine the 1 soliton 2 soliton and 3 soliton solutions of the kadomtsev petviashvili kp equation then the uniform formula of n soliton solutions is derived the method is simple and straightforward in constructing the n soliton of the nonlinear evolution equation in mathematical physics

localization in v dimensional incommensurate structures we exhibit a class of quasi periodic unbounded potential in thev dimensional discrete schrodinger equation for which the spectrum is only pure point with exponentially localized states and a dense set of eigenvalues in

new applications of variational iteration method abstract the variational iteration method is used for solving three types of nonlinear partial differential equations such as coupled schrodinger kdv generalized kdv and shallow water equations the exact and numerical solutions obtained by variational iteration method are compared with that obtained using adomian decomposition method the comparison shows that the two solutions obtained are excellent agreement the method is made showing that the former is more effective than the latter in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

soliton solutions and chaotic motions for the 2 1 dimensional zakharov equations in a laser induced plasma the 2 1 dimensional zakharov equations arising from the propagation of a laser beam in a plasma are studied in this paper analytic soliton solutions are obtained by means of the symbolic computation based on which we find that e is inversely related to p e but positively related to m i and c s while n is inversely related to p e and l but positively related to n 0 with e as the envelope of the high frequency electric field n as the plasma density while p e l n 0 m i and c s as the plasma electronic frequency frequency of the laser beam mean density of the plasma mass of an ion and ion sound velocity in the plasma respectively head on interaction is found to be transformed into an overtaking one with p e increasing or n 0 decreasing also period of the bound state interaction decreases with l decreasing considering the driving forces in the laser induced plasma we explore the associated chaotic motions as well as the effects of l p e k l n 0 m i c s f 1 and f 2 where k l is the wave number of the laser beam f 1 and f 1 represent the frequencies of driving forces respectively it is found that the chaotic motions can be weakened with p e c s and f 1 increasing or with n 0 m i and f 2 decreasing and the periodic motion can occur when f 1 reaches the critical value 2 while the chaotic motions are independent of l and k l

new exact solutions for solving the initial value problem of the kdv kp equation via the lie group method the traveling wave solutions of the two dimensional kdv kp equation are studied via the lie group method the kdv kp equation is a nonlinear partial differential equation in two spatial and one temporal coordinate which describes the evolution of nonlinear long waves of small amplitude with slow dependence on the transverse coordinate the investigation of exact solutions of the kdv kp via the application of lie group and the extended f expansion methods plays the main role in understanding the nonlinear physical phenomena

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

the cancellation theorem for projective modules over irrational rotation c algebras on montre que deux modules projectifs sur a qui sont isomorphes de facon stable sont en fait isomorphes

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

approximate analytical solution for seepage flow with fractional derivatives in porous media abstract in this paper a new and more exact model for seepage flow in porous media with fractional derivatives has been proposed which has modified the well known darcy law and overcome the continuity assumption of seepage flow a new kind of analytical method of nonlinear problem called the variational iteration method is described and used to give approximate solutions of the problem the results show that the proposed iteration method requiring no linearization or small perturbation is very effective and convenient

application of exp function method for 3 1 dimensional nonlinear evolution equations in this paper the exp function method is used to construct solitary and periodic solutions of nonlinear partial differential equations we choose an example which includes kadomstev petviashvili equation and potantial ytsf equation to illustrate the method the method is straightforward and concise and its applications are promising the exp function method presents a wider applicability for handling nonlinear wave equations

an improvement on the exp function method when balancing the highest order linear and nonlinear terms abstract the exp function method has been widely used to solve different kinds of nonlinear partial differential equations these nonlinear partial differential equations are transformed first into nonlinear ordinary differential equations and then the ansatz of the exp function method u n c p a n exp n m d q b m exp m is applied to obtain the solution however a part of the solution using this method is to construct the relations between c p d and q by balancing the highest order linear term with the highest order nonlinear term it is proved in the present paper that c d and p q are the only relations that can be obtained by applying this method to any nonlinear ordinary differential equation therefore the additional calculations of balancing the highest order linear term with the highest order nonlinear term are not longer required in future hence the method becomes more straightforward

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

a new riccati equation expansion method with symbolic computation to construct new travelling wave solution of nonlinear differential equations abstract in this paper based on a new system of riccati equations we present a triple riccati equation expansion method the nonlinear klein gordon equation and the combined kdv mkdv equation are chosen to illustrate the method as a result many new travelling solutions which include bell profile solitary wave solution singular solitary solutions periodic solutions are obtained this method can be used to the other nonlinear evolution equations in mathematics physics

spectral properties of a certain class of complex potentials in this paper we discuss spectral properties of the schroedinger operator a q on compact homogeneous spaces for certain complex valued potentials q we show for instance that for these potentials the spectrum of a q is identical with the spectrum of a introduction let g be a compact lie group and a the bi invariant laplacebeltrami operator on g fegan observed in f that there exist functions q on g for which the schroedinger operator q possesses an infinite sequence of eigenvalues al 2 such that each a is also an eigenvalue of a in this paper we will show that a potentials with this property exist not just on compact lie groups but on arbitrary compact homogeneous spaces as well and b for such potentials the entire spectrum of a q is identical with the spectrum of a in fegan s examples as well as in ours the potentials q are complex valued this means that the operator a q is not selfadjoint fortunately however there exists a rather nice spectral theory for such operators for instance their generalized eigenspaces are finite dimensional and span l2 see 2 below in view of this we were surprised to find relatively little material in the literature on such operators a notable exception is peter sarnack s beautiful paper on schroedinger operators with quasiperiodic q s see s we will describe and sketch the proof of our main result let g be a compact connected lie group h a closed subgroup and x the homogeneous space g h for simplicity we will assume for the moment that g is semisimple though this assumption is not essential see 4 for the case g s let g be the unitary dual of g we can order g lexicographically by choosing a system of positive weights consider the hilbert space direct sum 1 1 l2 x ha a eg ha being the g invariant subspace of l2 x on which g acts according to the representation a each irreducible subspace of ha possesses a unique maximal weight vector let h be the subspace of ha spanned by these vectors and let 1 2 l2 x ha received by the editors august 18 1982 and in revised form november 19 1982 1980 mathematics subject classification primary 58g25 secondary 35p99 research supported by the national university of mexico c1983 american mathematical society 0002 9947 83 1 00 25 per page

numerical solutions of nonlinear evolution equations using variational iteration method the variational iteration method is used to solve three kinds of nonlinear partial differential equations coupled nonlinear reaction diffusion equations hirota satsuma coupled kdv system and drinefel d sokolov wilson equations numerical solutions obtained by the variational iteration method are compared with the exact solutions revealing that the obtained solutions are of high accuracy he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomial in adomian method the method is straightforward and concise and it can also be applied to other nonlinear evolution equations in mathematical physics

a separable brown douglas fillmore theorem and weak stability we give a separable brown douglas fillmore theorem let a be a separable amenable c algebra which satisfies the approximate uct b be a unital separable amenable purely infinite simple c algebra and h 1 h 2 a b be two monomorphisms we show that h 1 and h 2 are approximately unitarily equivalent if and only if h 1 h 2 in kl a b we prove that for any e 0 and any finite subset f a there exist 0 and a finite subset g a satisfying the following for any amenable purely infinite simple c algebra b and for any contractive positive linear map l a b such that l ab l a l b 0 there is 0 such that in any unital amenable purely infinite simple c algebra b if uv e i vu for a pair of unitaries then there exists a pair of unitaries u 1 and v 1 in b such that u 1 v 1 e i v 1 u 1 u 1 u e and v 1 v e

oscillatory instability of traveling waves for a kdv burgers equation the stability of traveling wave solutions of a generalization of the kdv burgers equation o u u p o u 03u a o u is studied as the parameters p and a are varied the eigenvalue problem for the linearized evolution of perturbations is analyzed by numerically computing evans function d a an analytic function whose zeros correspond to discrete eigenvalues in particular the number of unstable eigenvalues in the complex plane is evaluated by computing the winding number of d a analytical and numerical evidence suggests that a hopf bifurcation occurs for oscillatory traveling wave profiles in certain parameter ranges dynamic simulations suggest that the bifurcation is subcritical no stable time periodic solution is found

approximate solution of nonlinear differential equations with convolution product nonlinearities in this paper a new iteration method is proposed to solve nonlinear problems special attention is paid to nonlinear differential equations with convolution product nonlinearities the results reveal the approximations obtained by the proposed method are uniformly valid for both small and large parameters in nonlinear problems furthermore the first order of approximations are more accurate than perturbation solutions at high order of approximation