smooth approximation of plurisubharmonic functions on almost complex manifolds this note establishes smooth approximation from above for j plurisubharmonic functions on an almost complex manifold x j the following theorem is proved suppose x is j pseudoconvex i e x admits a smooth strictly j plurisubharmonic exhaustion function let u be an upper semi continuous j plurisubharmonic function on x then there exists a sequence u j in c infty x of smooth strictly j plurisubharmonic functions point wise decreasing down to u in any almost complex manifold x j each point has a fundamental neighborhood system of j pseudoconvex domains and so the theorem above establishes local smooth approximation on x this result was proved in complex dimension 2 by the third author who also showed that the result would hold in general dimensions if a parallel result for continuous approximation were known this paper establishes the required step by solving the obstacle problem

soliton solutions of burgers equations and perturbed burgers equation abstract this paper carries out the integration of burgers equation by the aid of tanh method this leads to the complex solutions for the burgers equation kdv burgers equation coupled burgers equation and the generalized time delayed burgers equation finally the perturbed burgers equation in 1 1 dimensions is integrated by the ansatz method

the wightman axioms for the fermionic federbush model all wightman axioms including asymptotic completeness are proved for the federbush model with coupling constants in the range 1 2 1 2

scattering theory for the federbush massless thirring and continuum ising models the existence of the lsz limits of the positive energy quantum fields of the federbush thirring and ising models is proved the corresponding s matrices are obtained explicitly confirming previous formal results and are shown to result from a large class of dynamics the scattering theory for the federbush and thirring models on the classical and negative energy quantum levels is studied as well the wave and scattering operators are shown to exist and are obtained explicitly and they are proved to be shared by a large class of dynamics containing in particular the polynomial conserved charges

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

global existence and asymptotic behaviour of the solution of a generalized burger s equation with viscosity we obtain the global existence and uniqueness for a generalized burger s equation with viscosity and the initial value being in l by successive method moreover under certain condition on the initial value the solution tends to the solution of a linear heat equation in h1

critical limit one point correlations of monodromy fields on 321 1321 1321 1 monodromy fields on 2 are a family of lattice fields in two dimensions which are a natural generalization of the two dimensional ising field occurring in thec algebra approach to statistical mechanics a criterion for the critical limit one point correlation of the monodromy field a m at a 2 mathop lim limits s uparrow 1 left langle sigma a m right rangle is deduced for matrices m gl p having non negative eigenvalues

one dimensional stochastic burgers equation driven by levy processes abstract in this paper we proved the global existence and uniqueness of the strong weak and mild solutions for one dimensional burgers equation perturbed by a poisson form process a poisson form and q wiener process with the dirichlet bounded condition we also proved the existence of the invariant measure of these models

all traveling wave exact solutions of two kinds of nonlinear evolution equations abstract in this article we employ the complex method to obtain all meromorphic solutions of complex korteweg de vries kdv equation and the modified benjamin bona mahony mbbm equation at first then find out all traveling wave exact solutions of the eqs kdv and mbbm the idea introduced in this paper can be applied to other nonlinear evolution equations our results show that all rational and simply periodic solutions of the eqs kdv and mbbm are solitary wave solutions the complex method is simpler than other methods and there exist some rational solutions w 2 r 2 z and simply periodic solutions w 2 s 1 z which are not only new but also not degenerated successively by the elliptic function solutions we give some computer simulations to illustrate our main results

critical scaling for monodromy fields the large scale asymptotics of the correlations for a family of two dimensional lattice field theories is calculated at the critical temperature

symplectic manifolds with contact type boundaries an example of a 4 dimensional symplectic manifold with disconnected boundary of contact type is constructed a collection of other results about symplectic manifolds with contact type boundaries are derived using the theory ofj holomorphic spheres in particular the following theorem of eliashberg floer mcduff is proved if a neighbourhood of the boundary of v is symplectomorphic to a neighbourhood ofs2n 1 in standard euclidean space and if vanishes on all 2 spheres inv thenv is diffeomorphic to the ballb2n

polyfolds cobordisms and the strong weinstein conjecture abstract we prove the strong weinstein conjecture for closed contact manifolds that appear as the concave boundary of a symplectic cobordism admitting an essential local foliation by holomorphic spheres

1 soliton solution of the generalized kdv equation with generalized evolution this paper obtains the 1 soliton solution of three variants of the generalized kdv equation with generalized evolution the solitary wave ansatz is used to carry out the integration of such equation the parameter domain is also identified in the process a couple of conserved quantities are also calculated for each of these variants the numerical simulations are also carried out

gromov s compactness of pseudo holomorphic curves and symplectic geometry on utilise certaines idees de schoerr et uhlenbeck sur les equations aux derivees partielles pour demontrer la compacite de gromov des courbes pseudoholomorphes

topological 1 soliton solution of the generalized kdv equation with generalized evolution abstract in this paper the topological 1 soliton solution to the generalized korteweg de vries equation with generalized evolution will be obtained the solitary wave ansatz methods will be applied to obtain the solutions in the process the constraints relations between the soliton parameters will also be determined

analytic multi soliton solutions of the generalized burgers equation the most elementary ansatz of the double exp function method for finding exact double wave solutions can be produced by an extension of a two soliton ansatz in a fractional form the generalized burgers equation is used as an example and closed form analytic multi soliton solutions are obtained for the first time

weak and strong fillability of higher dimensional contact manifolds for contact manifolds in dimension three the notions of weak and strong symplectic fillability and tightness are all known to be inequivalent we extend these facts to higher dimensions in particular we define a natural generalization of weak fillings and prove that it is indeed weaker at least in dimension five while also being obstructed by all known manifestations of overtwistedness we also find the first examples of contact manifolds in all dimensions that are not symplectically fillable but also cannot be called overtwisted in any reasonable sense these depend on a higher dimensional analogue of giroux torsion which we define via the existence in all dimensions of exact symplectic manifolds with disconnected contact boundary

compactons solitons and periodic solutions for variants of the kdv and the kp equations studying solitons and solitons with compact support is of important significance in nonlinear phenomena in this paper we study nonlinear variants of the kdv and the kp equations with positive and negative exponents we employ the sine cosine algorithm to back up our analysis exact solutions with compactons solitons solitary patterns and periodic structures are obtained for these variants

exp function method for solving nonlinear evolution equations with higher order nonlinearity abstract in this paper the exp function method is used to obtain generalized solitary solutions of the generalized drinfel d sokolov wilson dsw system and the generalized 2 1 dimensional burgers type equation then some of the solitary solutions are converted to periodic solutions or hyperbolic function solutions by a simple transformation the results show that the exp function method is a powerful and convenient mathematical tool for solving nonlinear evolution equations with higher order nonlinearity

group analysis of kdv equation with time dependent coefficients we study the generalized kdv equation having time dependent variable coefficients of the damping and dispersion from the lie group theoretic point of view lie group classification with respect to the time dependent coefficients is performed the optimal system of one dimensional subalgebras of the lie symmetry algebras are obtained these subalgebras are then used to construct a number of similarity reductions and exact group invariant solutions including soliton solutions for some special forms of the equations

variants of the generalized kdv equation with compact and noncompact structures abstract in this paper nonlinear dispersive variants of the generalized kdv equation are investigated the compact and the noncompact physical structures are studied two general formulas for the focusing branch and the defocusing branch that are of substantial interest are formally derived

symplectic fixed points and holomorphic spheres letp be a symplectic manifold whose symplectic form integrated over the spheres inp is proportional to its first chern class on the loop space ofp we consider the variational theory of the symplectic action function perturbed by a hamiltonian term in particular we associate to each isolated invariant set of its gradient flow an abelian group with a cyclic grading it is shown to have properties similar to the homology of the conley index in locally compact spaces as an application we show that if the fixed point set of an exact diffeomorphism onp is nondegenerate then it satisfies the morse inequalities onp we also discuss fixed point estimates for general exact diffeomorphisms

solitary wave solutions for a coupled pair of mkdv equations propagation of weakly nonlinear long waves is studied within the framework of a system of two coupled modified korteweg de vries equations we investigate analytically and numerically the various families of soliton states for the considered model by scaling the functions and variables we find that the resulting coupled pair of equations has only one combined parameter this parameter depends on the wave speed and the coupling coefficient explicit analytical expressions for both of the symmetric and antisymmetric states are determined numerical method is derived to solve the proposed system many numerical tests have been conducted to study the behavior of the solution and the existence of the asymmetric soliton states is displayed numerically

the spectrum of the transfer matrix in the c algebra of the ising model at high temperatures we investigate the state on the fermion algebra which gives rise to the thermodynamic limit of the gibbs ensemble in the two dimensional ising model on a half lattice with nearest neighbour interaction it is shown that the operatorp in the gns space which performs the essential functions of the renormalized transfer matrix has a quasi particle structure

the structure of rational and ruled symplectic 4 manifolds this paper investigates the structure of compact symplectic 4 manifolds v w which contain a symplectically embedded copy c of s2 with nonnegative self intersection number such a pair v c w is called minimal if in addition the open manifold v c contains no exceptional curves i e symplectically embedded 2 spheres with self intersection 1 we show that every such pair v c w covers a minimal pair v c c which may be obtained from v by blowing down a finite number of disjoint exceptional curves in v c further the family of manifold pairs v c w under consideration is closed under blowing up and down we next give a complete list of the possible minimal pairs we show that v is symplectomorphic either to p2 with its standard form or to an s2 bundle over a compact surface with a symplectic structure which is uniquely determined by its cohomology class moreover this symplectomorphism may be chosen so that it takes c either to 2 a complex line or quadric in cp2 or in the case when v is a bundle to a fiber or section of the bundle department of mathematics state university of new york at stony brook stony brook new york 11794 3651 e mail address dusa math sunysb edu this content downloaded from 207 46 13 145 on wed 27 apr 2016 05 10 07 utc all use subject to http about jstor org terms

examples of symplectic structures in this paper we construct symplectic forms tilde omega k k geqq 0 on a compact manifold tilde y which have the same homotopy theoretic invariants but which are not diffeomorphic

on a c algebra approach to phase transition in the two dimensional ising model we investigate the state on thec algebra of pauli spins on a one dimensional lattice infinitely extended in both directions which gives rise to the thermodynamic limit of the gibbs ensemble in the two dimensional ising model with nearest neighbour interaction it is shown that the representation of the pauli spin algebra associated with the state is factorial above and at the known critical temperature while it has a two dimensional center below the critical temperature as a technical tool we derive a general criterion for a state of the pauli spin algebra corresponding to a fock state of the fermion algebra to be primary we also show that restrictions of two quasifree states of the fermion algebra to its even part are equivalent if and only if the projection operatorse1 ande2 on the direct sum of two copies of the basic hilbert space satisfy the following two conditions 1 e1 e2 is in the hilbert schmidt class 2 e1 1 e2 has an even dimension where the even oddness of dime1 1 e2 is called 2 index ofe1 ande2 and is continuous ine1 ande2 relative to the norm topology

the dirichlet problem for nonlinear second order elliptic equations ii complex monge ampere and uniformaly elliptic equations on considere le probleme de dirichlet pour des equations elliptiques non lineaires d ordre 2 pour une fonction reelle dans un domaine borne de r n a frontiere lisse

symplectic diffeomorphisms and the flux homomorphism let x be a connected smooth manifold without boundary we will write difff ox for the group of all compactly supported diffeomorphisms of x which preserve the symplectic form o2 topologized as usual as the direct limit of the subgroups diff x of all diffeomorphisms with support in the fixed compact set k let diff oox be its identity component the flux is locally a homomorphism from a neighbourhood of the identity in diffo ox to h x r see calabi 6 it gives rise to a global homomorphism s o from the universal cover of difffo0x to hi x f and hence to a homomorphism

the monge ampere equation on almost complex manifolds we study the dirichlet problem for the monge ampere equation on almost complex manifolds we obtain the existence of the unique smooth solution in strictly pseudoconvex domains

dynamics in spectral solutions of burgers equation for low values of the viscosity coefficient burgers equation can develop sharp discontinuities which are difficult to simulate in a computer oscillations can occur by discretization through spectral collocation methods due to gibbs phenomena under a dynamic point of view these instabilities are related to bifurcations arising to the discretized equation for different values of discretized points herein a study is performed of the dynamics and bifurcations occurring in the spectral solutions of burgers equation with symmetry several phenomena are observed from limit cycles strange attractors to the presence of bistability with two periodic attractors with a periodic attractor and a strange attractor and with two strange attractors also other stable equilibrium points can occur diverse from the ones corresponding to the solution of burgers equation