long time dynamics for semi relativistic nls and half wave in arbitrary dimension we consider the cauchy problems associated with semi relativistic nls snls and half wave hw in particular we focus on the following two main questions local global cauchy theory existence and stability instability of ground states in between other results we prove the existence and stability of ground states for snls in the l 2 supercritical regime this is in sharp contrast with the instability of ground states for the corresponding hw which is also established along the paper by showing an inflation of norms phenomenon concerning the cauchy theory we show under radial symmetry assumption the following results a local existence result in h 1 for energy subcritical nonlinearity and a global existence result in the l 2 subcritical regime

group classification of linear evolution equations abstract the group classification problem for the class of 1 1 dimensional linear rth order evolution equations is solved for arbitrary values of r 2 it is shown that a related maximally gauged class of homogeneous linear evolution equations is uniformly semi normalized with respect to linear superposition of solutions and hence the complete group classification can be obtained using the algebraic method we also compute exact solutions for equations from the class under consideration using lie reduction and its specific generalizations for linear equations

global well posedness and scattering for the defocusing l 2 critical nonlinear schrodinger equation when d 2 in this article we prove that the defocusing cubic nonlinear schrodinger initial value problem is globally well posed and scattering for u0 l2 r2 the proof uses the bilinear estimates of planchon and vega and a frequency localized interaction morawetz estimate similar to the high frequency estimate of colliander keel staffilani takaoka and tao and especially the low frequency estimate of dodson

generalized strichartz estimates and scattering for 3d zakharov system we obtain scattering for the 3d zakharov system with non radial small data in the energy space with angular regularity of degree one the main ingredient is a generalized strichartz estimate for the schrodinger equation in the space of l2 angular integrability

nonlinear small data scattering for the wave and klein gordon equation on etudie l operateur diffusion qui appartient a la paire d equations u tt au f u 0 et u tt au 0 a represente l operateur j 1 n 2 x j 2 m 2 m r et f u u 1 u ou r 1

n dimensional equations with the maximum number of symmetry generators the authors obtain the general class of ordinary differential equations that can be reduced by a point transformation to the free particle equation and given the general form of the lie symmetry generators for these equations they apply these results to obtain the symmetry generators for the n dimensional harmonic oscillator and for a particle in a constant magnetic field

symmetries of linear systems of second order ordinary differential equations in this paper several problems concerning the lie algebra structure of symmetries and variational symmetries of a general linear system of second order ordinary differential equations are studied in particular a necessary and sufficient condition is obtained in terms of the coefficients of the system for the system s symmetry algebra to be of maximal dimension i e n2 4n 3 and isomorphic to sl n 2 r the well known symmetry algebra of the free particle equation x 0 when this condition is satisfied it is proved that the system is lagrangian and that its variational symmetry algebra is isomorphic to a fixed n2 3n 6 2 dimensional lie algebra whose structure levi mal cev decomposition and realization by means of a matrix algebra is determined for the particular case of isotropic systems which includes as far as is known all the examples treated in the literature explicit formulas for the generators of both the symmetry algebra and the variational symmetry algebra are obtained

local smoothing properties of dispersive equations is it possible for time evolution partial differential equations which are reversible and conservative to smooth locally the initial data for the linear wave equation for instance the answer is no however in 10 t kato found a local smoothing property of the korteweg de vries equation the solution of the initial value problem is locally one derivative smoother than the initial datum kato s proof uses in a curcial way the algebraic properties of the symbol for the korteweg de vries equation and the fact that the underlying spatial dimension is one actually judging from the way several integrations by parts and cancellations conspire to reveal a smoothing effect one would be inclined to believe this was a special property of the k dv equation this is not however the case in this paper we attempt to describe a general local smoothing effect for dispersive equations and systems the smoothing effect is due to the dispersive nature of the linear part of the equation all the physically significant dispersive equations and systems known to us have linear parts displaying this local smoothing property to mention only a few the k dv benjamin ono intermediate long wave various boussinesq and schrodinger equations are included we study thus equations and systems of the form

on some schrodinger and wave equations with time dependent potentials the existence and uniqueness of solutions in the initial value problem for schrodinger and wave equations in the presence of a large time dependent potential is studied the usual strichartz estimates for such linear evolutions are shown to hold true with optimal assumptions on the potentials as a byproduct one obtains a counterexample to the two dimensional double endpoint inhomogeneous strichartz estimate

strichartz estimates in the frame of modulation spaces abstract in this paper we study the strichartz estimates for three types of differential equations in the framework of modulation spaces the equations considered here include the wave equation the schrodinger equation and the nonelliptic schrodinger equation inhomogeneous equations of the above three types are also studied

the radial defocusing energy supercritical nls in dimension four abstract we consider the radial defocusing nonlinear schrodinger equations i u t u u p u with supercritical exponent p 4 in four space dimensions and prove that any radial solution that remains bounded in the critical sobolev space must be global and scatter

metaplectic representation on wiener amalgam spaces and applications to the schrodinger equation we study the action of metaplectic operators on wiener amalgam spaces giving upper bounds for their norms as an application we obtain new fixed time estimates in these spaces for schrodinger equations with general quadratic hamiltonians and strichartz estimates for the schrodinger equation with potentials v x x 2

strichartz inequalities and the nonlinear schrodinger equation on compact manifolds kklwe prove strichartz estimates with fractional loss of derivatives for the schrodinger equation on any riemannian compact manifold as a consequence we infer low regularity local well posedness results in any dimension as well as global existence results for the cauchy problem of nonlinear schrodinger equations on surfaces in the case of defocusing polynomial nonlinearities and on three manifolds in the case of cubic defocusing nonlinearities we also discuss the optimality of these strichartz estimates on spheres

the focusing energy critical nonlinear schrodinger equation in dimensions five and higher we consider the focusing energy critical nonlinear schr odinger equation iu t delta u u 4 over d 2 u in dimensions d geq 5 we prove that if a maximal lifespan solution u colon i times bbb r d to bbb c obeys sup t in i nabla u t 2 nabla w 2 then it is global and scatters both forward and backward in time here w denotes the ground state which is a stationary solution of the equation in particular if a solution has both energy and kinetic energy less than those of the ground state w at some point in time then the solution is global and scatters we also show that any solution that blows up with bounded kinetic energy must concentrate at least the kinetic energy of the ground state similar results were obtained by kenig and merle for spherically symmetric initial data and dimensions d 3 4 5

global well posedness and scattering for the defocusing l 2 critical nonlinear schrodinger equation when d 1 in this paper we prove global well posedness and scattering for the defocusing one dimensional mass critical nonlinear schr o dinger equation we make use of a long time strichartz estimate and a frequency localized morawetz estimate this continues work begun in earlier papers for dimensions d geq 3 and d 2

maximum sum rate of repeat accumulate interleave division system by fixed point analysis a multi user repeat accumulate interleave division raid system is considered for a multiple access channel mac with binary inputs equal power and symbol synchronization in the system a regular repeat accumulate ra code serially concatenated with block spreading is employed for each user at the receiver multi user message passing decoding is performed on a single factor graph over the mac with additive white gaussian noise awgn a fixed point analysis is developed to obtain the optimal code rate and the spreading length that give the maximum sum rate for an arbitrary small decoding error rate

analytic smoothing effect for the schrodinger equation with long range perturbation we study microlocal analytic singularity of solutions to schr odinger equation with analytic coefficients using microlocal weight estimate developped for estimating the phase space tunneling we prove microlocal smoothing estimates that generalize results by l robbiano and c zuily we suppose the schr odinger operator is a long range type perturbation of the laplacian and we employ positive commutator type estimates to prove the smoothing property

generalized strichartz inequalities for the wave equation strichartz inequalities for the wave equation u f are estimates of the solution u of the cauchy problem for that equation in the form of space time integral norms in terms of similar norms of the inhomogeneity f and of suitable norms of the initial data

final state problem for a quadratic nonlinear schrodinger system in two space dimensions with mass resonance abstract we consider the asymptotic behavior of a solution to a quadratic nonlinear schrodinger system in two space dimensions we construct a particular solution which describes the charge dissipation phenomenon in spite of the mass preserving structure of the system this is a consequence of a new explicit solution to a system of ordinary differential equation which approximates asymptotic behavior of a solution to the system

integrability of systems of two second order ordinary differential equations admitting four dimensional lie algebras we suggest an algorithm for integrating systems of two second order ordinary differential equations with four symmetries in particular if the admitted transformation group has two second order differential invariants the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation otherwise the systems reduce to partially uncoupled forms and can also be integrated by quadratures

a counter example to strichartz estimates for the inhomogeneous schrodinger equation abstract we disprove strichartz estimates for the solution of the inhomogeneous schrodinger equation in a certain range of the lebesgue exponents values

sl 3 r realisations and the damped harmonic oscillator the point and contact lie groups for the damped harmonic oscillator are found and several realisations of the sl 3 r lie group are analysed the non critical and critical cases are studied separately and a sort of limiting procedure is defined which leaves the lie algebra structure unchanged some physical applications of these results are also pointed out

strichartz estimates for schrodinger equations on irrational tori in this paper we prove new strichartz estimates for linear schrodinger equations posed on d dimensional irrational tori then we use these estimates to prove subcritical and critical local well posedness results for nonlinear schrodinger equations on irrational tori

analysis of sum product decoding of low density parity check codes using a gaussian approximation density evolution is an algorithm for computing the capacity of low density parity check ldpc codes under message passing decoding for memoryless binary input continuous output additive white gaussian noise awgn channels and sum product decoders we use a gaussian approximation for message densities under density evolution to simplify the analysis of the decoding algorithm we convert the infinite dimensional problem of iteratively calculating message densities which is needed to find the exact threshold to a one dimensional problem of updating the means of the gaussian densities this simplification not only allows us to calculate the threshold quickly and to understand the behavior of the decoder better but also makes it easier to design good irregular ldpc codes for awgn channels for various regular ldpc codes we have examined thresholds can be estimated within 0 1 db of the exact value for rates between 0 5 and 0 9 codes designed using the gaussian approximation perform within 0 02 db of the best performing codes found so far by using density evolution when the maximum variable degree is 10 we show that by using the gaussian approximation we can visualize the sum product decoding algorithm we also show that the optimization of degree distributions can be understood and done graphically using the visualization

global parametrices and dispersive estimates for variable coefficient wave equations in this article we consider variable coefficient time dependent wave equations in mathbb r times mathbb r n using phase space methods we construct outgoing parametrices and prove strichartz type estimates globally in time this is done in the context of c 2 metrics which satisfy a weak asymptotic flatness condition at infinity

strichartz estimates for the magnetic schrodinger equation abstract we prove global scale invariant strichartz estimates for the linear magnetic schrodinger equation with small time dependent magnetic field this is done by constructing an appropriate parametrix as an application we show a global regularity type result for schrodinger maps in dimensions n 6

solitons and scattering for the cubic quintic nonlinear schrodinger equation on mathbb r 3 r 3 we consider the cubic quintic nonlinear schrodinger equation i partial t u delta u u 2u u 4u in the first part of the paper we analyze the one parameter family of ground state solitons associated to this equation with particular attention to the shape of the associated mass energy curve additionally we are able to characterize the kernel of the linearized operator about such solitons and to demonstrate that they occur as optimizers for a one parameter family of inequalities of gagliardo nirenberg type building on this work in the latter part of the paper we prove that scattering holds for solutions belonging to the region mathcal r of the mass energy plane where the virial is positive we show that this region is partially bounded by solitons also by rescalings of solitons which are not soliton solutions in their own right the discovery of rescaled solitons in this context is new and highlights an unexpected limitation of any virial based methodology

design of regular 2 d sub c ldpc codes over gf q using their binary images in this paper a method to design regular 2 dc ldpc codes over gf q with both good waterfall and error floor properties is presented based on the algebraic properties of their binary image first the algebraic properties of rows of the parity check matrix h associated with a code are characterized and optimized to improve the waterfall then the algebraic properties of cycles and stopping sets associated with the underlying tanner graph are studied and linked to the global binary minimum distance of the code finally simulations are presented to illustrate the excellent performance of the designed codes

analytic wave front set for solutions to schrodinger equations this paper is a continuation of a martinez s nakamura v sordoni analytic smoothing effect for the schrodinger equation with long range perturbation comm pure appl math lix 2006 1330 1351 where an analytic smoothing effect was proved for long range type perturbations of the laplacian h0 on rn in this paper we consider short range type perturbations h of the laplacian on rn and we characterize the analytic wave front set of the solution to the schrodinger equation e ithf in terms of that of the free solution e ith0f for t 0 in the backward non trapping region this result is an analytic analogue of results by hassel and wunsch a hassel j wunsch the schrodinger propagator for scattering metrics ann of math 162 2005 487 523 and nakamura s nakamura wave front set for solutions to schrodinger equations j funct anal 256 2009 1299 1309

endpoint strichartz estimates we prove an abstract strichartz estimate which implies previously unknown endpoint strichartz estimates for the wave equation in dimension n 4 and the schrodinger equation in dimension n 3 three other applications are discussed local existence for a nonlinear wave equation and strichartz type estimates for more general dispersive equations and for the kinetic transport equation

some new strichartz estimates for the schrodinger equation abstract we deal with fixed time and strichartz estimates for the schrodinger propagator as an operator on wiener amalgam spaces we discuss the sharpness of the known estimates and we provide some new estimates which generalize the classical ones as an application we present a result on the wellposedness of the linear schrodinger equation with a rough time dependent potential

the global cauchy problem for the non linear klein gordon equation on demontre l unicite de solutions faibles et l existence et l unicite de solutions globales fortement continues dans l espace energie

parametrices and dispersive estimates for schrodinger operators with variable coefficients in this article we consider variable coefficient time dependent schr odinger evolutions in bbb r n using phase space methods we construct outgoing parametrices and prove strichartz type estimates globally in time this is done in the context of c 2 metrics which satisfy a weak asymptotic flatness condition at infinity

asymptotic stability of breathers in some hamiltonian networks of weakly coupled oscillators we consider a hamiltonian chain of weakly coupled anharmonic oscillators it is well known that if the coupling is weak enough then the system admits families of periodic solutions exponentially localized in space breathers in this paper we prove asymptotic stability in energy space of such solutions the proof is based on two steps first we use canonical perturbation theory to put the system in a suitable normal form in a neighborhood of the breather second we use dispersion in order to prove asymptotic stability the main limitation of the result rests in the fact that the nonlinear part of the on site potential is required to have a zero of order 8 at the origin from a technical point of view the theory differs from that developed for hamiltonian pdes due to the fact that the breather is not a relative equilibrium of the system

coding theorems for turbo code ensembles this paper is devoted to a shannon theoretic study of turbo codes we prove that ensembles of parallel and serial turbo codes are good in the following sense for a turbo code ensemble defined by a fixed set of component codes subject only to mild necessary restrictions there exists a positive number spl gamma sub 0 such that for any binary input memoryless channel whose bhattacharyya noise parameter is less than spl gamma sub 0 the average maximum likelihood ml decoder block error probability approaches zero at least as fast as n sup spl beta where spl beta is the interleaver gain exponent defined by benedetto et al in 1996

quintic nls in the exterior of a strictly convex obstacle we consider the defocusing energy critical nonlinear schr odinger equation in the exterior of a smooth compact strictly convex obstacle in three dimensions for the initial value problem with dirichlet boundary condition we prove global well posedness and scattering for all initial data in the energy space

local smoothing property and strichartz inequality for schrodinger equations with potentials superquadratic at infinity abstract we study smoothing properties for time dependent schrodinger equations i u t 1 2 u v x u u 0 l 2 r n with potentials which satisfy v x o x m at infinity m 2 we show that the solution u t x is 1 m times differentiable with respect to x at almost all t r and explain that this is the result of the fact that the sojourn time of classical particles with energy in arbitrary compact set is less than ct 1 m during 0 t when is very large we also show strichartz s inequality with derivative loss for such potentials and give its application to nonlinear schrodinger equations

spectral efficiency of cdma with random spreading the cdma channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods furthermore its analysis provides a comparison baseline for cdma channels with deterministic signature waveforms spanning one symbol period we analyze the spectral efficiency total capacity per chip as a function of the number of users spreading gain and signal to noise ratio and we quantify the loss in efficiency relative to an optimally chosen set of signature sequences and relative to multiaccess with no spreading white gaussian background noise and equal power synchronous users are assumed the following receivers are analyzed a optimal joint processing b single user matched filtering c decorrelation and d mmse linear processing

on quadratic derivative schrodinger equations in one space dimension we consider the schrodinger equation with derivative perturbation terms in one space dimension for the linear equation we show that the standard strichartz estimates hold under specific smallness requirements on the potential as an application we establish existence of local solutions for quadratic derivative schrodinger equations in one space dimension with small and rough cauchy data

smoothing properties and retarded estimates for some dispersive evolution equations smoothing properties in the form of space time integrability properties play an important role in the study of dispersive evolution equations a number of them follow from a combination of general arguments and specific estimates we present a general formulation which makes the separation between the two types of ingredients as clear as possible and we illustrate it with the examples of the schrodinger equation of the wave equation and of a class of 1 1 dimensional equations related to the benjamin ono equation of special interest for the cauchy problem are retarded estimates expressed in terms of those properties we derive a number of such estimates associated with the last example and we mention briefly an application of those estimates to the cauchy problem for the generalized benjamin ono equation

global existence and scattering for rough solutions of a nonlinear schr odinger equation on r 3 we prove global existence and scattering for the defocusing cubic nonlinear schrodinger equation in h s r 3 for s 4 the main new estimate in the argument is a morawetz type inequality for the solution this estimate bounds k x t k l 4 r3 r whereas the well known morawetz type estimate of lin strauss controls r 1 0 r r3 x t 4 x dxdt

contact symmetries of general linear second order ordinary differential equations using 1 1 mappings the complete symmetry groups of contact transformations of general linear second order ordinary differential equations are determined from two independent solutions of those equations and applied to the harmonic oscillator with and without damping

finite field spreading for multiple access channel as a generalization of the binary spreading scheme in conventional direct sequence code division multiple access ds cdma and interleave division multiple access idma a finite field spreading scheme is proposed for a synchronous multiple access channel mac with gaussian noise and equal power users for each user each information symbol over a finite field is spread into a length l field vector by l field multiplications at the receiver an iterative multi user decoding algorithm on a factor graph is developed to recover each user s information symbol to estimate the bit error rate performance of an uncoded finite field spreading system an extrinsic information transfer analysis of the finite field despreading is given this analysis shows that in addition to overcoming multi user interference the finite field spreading scheme can also provide an additional coding gain to overcome gaussian noise compared with the conventional spreading scheme this coding gain increases with the field order the finite field spreading serially concatenated with a nonbinary low density parity check ldpc code with field order 64 approaches the mac capacity within 0 26 db at a sum rate of 0 25

quantization of quadratic lienard type equations by preserving noether symmetries abstract the classical quantization of a family of a quadratic lienard type equation lienard ii equation is achieved by a quantization scheme nucci 2011 28 that preserves the noether point symmetries of the underlying lagrangian in order to construct the schrodinger equation this method straightforwardly yields the schrodinger equation as given in choudhury and guha 2013 6

on scattering and everywhere defined scattering operators for nonlinear klein gordon equations asymptotic properties of solutions of the nonlinear klein gordon equation t2u u m2u f u 0 nlkg u 0 tu 0 are investigated which are inherited from the corresponding solutions v of the linear klein gordon equation t2v v m2v 0v 0 tv 0 kg in particular the finiteness of time integrals in lq over r of certain sobolevnorms in space of the solution is proved to be such a hereditary property together with a device by w a strauss and a weak decay result for the kg due to r s strichartz this is used to prove that under suitable restrictions on the nonlinearity the scattering operator for the nlkg is defined on all of l21 l2 for n 3

dynamics for the energy critical nonlinear schrodinger equation in high dimensions in t duyckaerts f merle dynamic of threshold solutions for energy critical nls preprint arxiv 0710 5915 math ap t duyckaerts and f merle studied the variational structure near the ground state solution w of the energy critical nls and classified the solutions with the threshold energy e w in dimensions d 3 4 5 under the radial assumption in this paper we extend the results to all dimensions d 6 the main issue in high dimensions is the non lipschitz continuity of the nonlinearity which we get around by making full use of the decay property of w

on the lie symmetries of the classical kepler problem the standard version of noether s theorem when applied to the classical kepler problem leads to the constants of energy and angular momentum but does not give the hidden symmetry known as the runge lenz vector lie s theory of differential equations is used to obtain all three constants of motion the transformations of solutions under the point transformations to which these constants correspond are studied the results are generalised to n dimensions

calogero s goldfish is indeed a school of free particles a many body system of n nonlinear ordinary differential equations of second order which is amenable to exact treatments a goldfish calogero 2001 the neatest many body problem amenable to exact treatments a goldfish physica d 152 153 78 84 is shown to be equivalent through an exact transformation to the equations of one dimensional motion of n 1 free particles a school of free particles indeed the transformation is obtained by applying the reduction method and lie group analysis as introduced in nucci 1996 the complete kepler group can be derived by lie group analysis j math phys 37 1772 5

smoothing properties and existence of solutions for the generalized benjamin ono equation abstract we study the cauchy problem for the generalized benjamin ono equation tu d d 2 u dv u where d d dx u 0 and v e 1 r r with v 0 v 0 0 using commutator identities and estimates we prove that the equation exhibits smoothing properties similar to those of the generalized korteweg de vries equation gkdv which is the special case 1 of if v satisfies suitable estimates at zero and at infinity we prove that the cauchy problem for the equation with initial data u 0 u0 has a solution u l r l2 l2loc r h loc if u0 l2 and has a solution u l r h l2loc r h2 loc if u0 h finite energy solution in addition we prove that the usual benjamin ono equation 1 2 v u u 2 has a solution u l r h1 l2loc r h 3 2 loc for u0 h1 those results are easily extended to related equations such as the intermediate long wave equation or the smith equation

global well posedness and scattering for the mass critical nonlinear schrodinger equation with mass below the mass of the ground state abstract in this paper we prove that the focusing d dimensional mass critical nonlinear schrodinger initial value problem is globally well posed and scattering for u 0 l 2 r d u 0 l 2 r d q l 2 r d where q is the ground state and d 1 we first establish an interaction morawetz estimate that is positive definite when u 0 l 2 r d q l 2 r d and has the appropriate scaling next we will prove an interaction morawetz estimate localized to low frequencies similar to the estimates made in 13 14 15 see also 12 for localization to high frequencies in the energy critical case

strichartz estimates and maximal operators for the wave equation in r3 abstract we prove sharp strichartz type estimates in three dimensions including some which hold in reverse space time norms for the wave equation with potential these results are also tied to maximal operator estimates studied by rogers villarroya of which we prove a sharper version as a sample application we use these results to prove the local well posedness and the global well posedness for small initial data of semilinear wave equations in r 3 with quintic or higher monomial nonlinearities

the defocusing energy supercritical nls in four space dimensions abstract we consider a class of defocusing energy supercritical nonlinear schrodinger equations in four space dimensions following a concentration compactness approach we show that for 1 s c 3 2 any solution that remains bounded in the critical sobolev space h x s c r 4 must be global and scatter key ingredients in the proof include a long time strichartz estimate and a frequency localized interaction morawetz inequality

infinitesimal symmetry transformations ii some one dimensional nonlinear systems the converse problem of similarity analysis is discussed for the infinitesimal symmetry transformations of ordinary second order differential equations which are nonlinear in x and may be linear or nonlinear in x a natural classification of the problem arises according to the highest order n of nonlinearity in x the completely general maximal lie algebra is obtained for the case n 3 in the case n 4 one has besides the system of differential equations for the infinitesimal generators an extra set of anholonomic constraints which operates as a symmetry breaking mechanism producing a strong reduction in the number of surviving parameters miscellaneous examples are given which illustrate some features of similarity analysis of nonlinear systems the infinitesimal point transformation symmetries of the van der pol oscillator are also briefly discussed

nonlocal models for nonlinear dispersive waves abstract considered herein are model equations for the unidirectional propagation of small amplitude nonlinear dispersive long waves such as those governed by the classical korteweg de vries equation of special interest are physical situations in which the linear dispersion relation is not appropriately approximated by a polynomial so that the operator modelling dispersive effect is nonlocal particular cases in view here are the benjamin ono equation and the intermediate long wave equation which arise in internal wave theory and smith s equation which governs certain types of continental shelf waves the initial value problem for these equations is shown to be globally well posed in the classical sense including continuous dependence upon the initial data and in certain cases upon the modelling of nonlinear and dispersive effects whilst the results are stated for the specific equations listed above the techniques utilized are seen to have a considerable range of generality as regards application to nonlinear dispersive evolution equations particularly worthy of note is our theorem implying that solutions of the intermediate long wave equation converge strongly to solutions of the korteweg de vries equation or to solutions of the benjamin ono equation in appropriate asymptotic limits

on the local well posedness for the nonlinear schrodinger equation with spatial variable coefficient abstract we study a new type of nonlinear schrodinger equation where the coefficient of laplacian depends on spatial variable based on a modified hankel transform and delicate frequency estimates we establish the local well posedness of the nls with spatial variable coefficient in the weighted lebesgue space for n 2 and extend the strichartz estimates to the non radially schrodinger equation with spatial variable coefficient in 2d euclidian space

almost sure local well posedness and scattering for the 4d cubic nonlinear schrodinger equation abstract we consider the cauchy problem for the defocusing cubic nonlinear schrodinger equation in four space dimensions and establish almost sure local well posedness and conditional almost sure scattering for random initial data in h x s r 4 with 1 3 s 1 the main ingredient in the proofs is the introduction of a functional framework for the study of the associated forced cubic nonlinear schrodinger equation which is inspired by certain function spaces used in the study of the schrodinger maps problem and is based on strichartz spaces as well as variants of local smoothing inhomogeneous local smoothing and maximal function spaces additionally we prove an almost sure scattering result for randomized radially symmetric initial data in h x s r 4 with 1 2 s 1

mixed norm strichartz type estimates for hypersurfaces in three dimensions in their work ikromov and muller fourier restriction for hypersurfaces in three dimensions and newton polyhedra princeton university press princeton 2016 proved the full range l p l 2 fourier restriction estimates for a very general class of hypersurfaces in mathbb r 3 which includes the class of real analytic hypersurfaces in this article we partly extend their results to the mixed norm case where the coordinates are split in two directions one tangential and the other normal to the surface at a fixed given point in particular we resolve completely the adapted case and partly the non adapted case in the non adapted case the case when the linear height h text lin phi is below two is settled completely

on the group classiﬁcation of systems of two linear second order ordinary differential equations with constant coeﬃcients copyright 2014 elsevier due to copyright restrictions only the abstract is available for access to the full text item please consult the publisher s website the definitive version of the work is published in journal of mathematical analysis and applications february 2014 vol 410 pages 341 347

achievable information rates and the coding spreading tradeoff in finite sized synchronous cdma systems in this letter we compute achievable information rates for finite sized synchronous code division multiple access cdma systems and low density parity check ldpc codes are adopted to approach the achievable rates the associated coding spreading tradeoff problem is also considered using these results we assume binary random spreading sequences and the computed achievable rates are averaged over ensembles of spreading sequences unlike most prior papers which analyze the spectral efficiency of large cdma systems under gaussianity assumptions channel inputs and or multiple access interference we make no such assumptions in order to display the coding spreading tradeoff we plot the minimum required signal to noise ratio for reliable transmission as a function of information rate it is shown that the coding spreading tradeoff favors all coding i e no spreading when the optimal joint multiuser detector decoder is employed whereas for systems with a suboptimal multiuser detector and single user decoders there generally exists an optimal balance between coding and spreading we also provide simulation results on the performance of ldpc coded synchronous cdma systems which approach the information theoretic limits we have computed

blow up of solutions to the nonlinear schrodinger equations on manifolds in this paper we partially settle down the long standing open problem of the finite time blow up property about the nonlinear schrodinger equations on some riemannian manifolds such as the standard 2 sphere s2 and the hyperbolic 2 space h2 1 using the similar idea we establish such blow up results on higher dimensional standard sphere and hyperbolic n space extensions to n dimensional riemannian warped product manifolds with n 2 are also given

characteristic functional structure of infinitesimal symmetry mappings of classical dynamical systems iv classical velocity independent mappings of second order differential equations in a recent paper j math phys 26 3080 1985 the first of this series it was shown that velocity dependent symmetry mappings of second order dynamical systems have a characteristic functional structure which is the same for all dynamical systems the present paper continues the investigation of this characteristic functional structure a shortened improved conceptionally simpler proof of the existence of the characteristic structure is given it is shown how this characteristic functional structure may be formally incorporated into a new procedure for the determination of classical velocity independent symmetries of dynamical systems in addition to providing insight into symmetry analysis this new procedure is also a practical alternative to existing symmetry methods for those dynamical systems for which there exist sufficient knowledge of the form of the dynamical solution so that it is feasible to determine constants of motion by inversion or the converse application of the procedure to

generalizations of noether s theorem in classical mechanics in this paper a review is presented of various approaches to the generalization of the version of noether s theorem which is presented in most textbooks on classical mechanics its motivation is the controversy still persisting around the possible scope of a noether type theorem allowing for velocity dependent transformations our analysis is centered around the one factor common to all known treatments namely the structure of the related first integral we first discuss the most general framework in which a function of the above mentioned structure constitutes a first integral of a given lagrangian system and show that one cannot really talk about an interrelationship between symmetries and first integrals there we then compare different proposed generalizations of noether s theorem by describing the nature of the restrictions which characterize them when they are situated within the broadest framework we prove a seemingly new equivalence result between the two main approaches that of invaria

the focusing energy critical hartree equation abstract we consider the focusing energy critical nonlinear hartree equation i u t u x 4 u 2 u we proved that if a maximal lifespan solution u i r d c satisfies sup t i u t 2 w 2 where w is the static solution of the equation then the maximal lifespan i r moreover the solution scatters in both time directions for spherically symmetric initial data similar result has been obtained in c miao g xu l zhao global wellposedness scattering and blowup for the energy critical focusing hartree equation in the radial case colloq math in press the argument is an adaptation of the recent work of r killip and m visan r killip m visan the focusing energy critical nonlinear schrodinger equation in dimensions five and higher preprint on energy critical nonlinear schrodinger equations

existence of solutions for schrodinger evolution equations we study the existence uniqueness and regularity of the solution of the initial value problem for the time dependent schrodinger equationi u t 1 2 u v t x u u 0 u0 we provide sufficient conditions onv t x such that the equation generates a unique unitary propagatoru t s and such thatu t s u0ec1 l2 c0 h2 n foru0eh2 n the conditions are general enough to accommodate moving singularities of type x 2 n 4 or x n 2 n 3

lie symmetries of systems of second order linear ordinary differential equations with constant coefficients lie symmetries of systems of second order linear ordinary differential equations with constant coefficients are exhaustively described over both the complex and real fields the exact lower and upper bounds for the dimensions of the maximal lie invariance algebras possessed by such systems are obtained using an effective algebraic approach

well posedness of the initial value problem for the korteweg de vries equation 1 1 itu axu u1xu o x t e r u x 0 uo x the kdv equation which was first derived as a model for unidirectional propagation of nonlinear dispersive long waves 21 has been considered in different contexts namely in its relation with the inverse scattering method in plasma physics and in algebraic geometry see 24 and references therein our purpose is to study local and global well posedness of the ivp 1 1 in classical sobolev spaces hs r we shall say that the ivp 1 1 is locally resp globally well posed in the function space x if it induces a dynamical system on x by generating a continuous local resp global flow it was established in the works of bona and smith 3 bona and scott 2 saut and temam 30 and kato 1 5 that the ivp 1 1 is locally resp globally well posed in hs with s 3 2 resp s 2 roughly speaking global well posedness in hs depends on the available local theory and on the conservation laws satisfied by solutions of 1 1 namely

linearization criteria for a system of two second order ordinary differential equations for a system of second order ordinary differential equations conditions of linearizability to the form x 0 are well known however an arbitrary linear system need not be equivalent via an invertible point transformation to this simple form we provide the criteria for a system of two second order equations to be mapped to the linear system of the general form necessary and sufficient conditions for linearization by means of a point transformation are given in terms of coefficients of the system these results are illustrated with a number of examples

distance enumerator analysis for interleave division multi user codes consider an interleave division multi user coding model for a gaussian multiple access channel mac each user s message is encoded by a separate channel encoder followed by a user interleaver which is employed for user separation all the users codewords are jointly regarded as one multi user codeword and the distance between two multi user codewords is defined as the euclidean distance after the inter user superposition caused by the mac a distance enumerator analysis estimates the multi user maximum likelihood decoding performance by introducing user scramblers a multi user code ensemble is defined and its distance enumerator is calculated as concatenated multiple single user codes and a superposition code both finite length and asymptotic analyses are given and it is shown that interleave division multi user codes have much better distance properties than conventional random direct sequence code division multiple access in fact the codes achieve almost the same asymptotic uniquely decodable performance as a multi user random code

unveiling turbo codes some results on parallel concatenated coding schemes a parallel concatenated coding scheme consists of two simple constituent systematic encoders linked by an interleaver the input bits to the first encoder are scrambled by the interleaver before entering the second encoder the codeword of the parallel concatenated code consists of the input bits to the first encoder followed by the parity check bits of both encoders this construction can be generalized to any number of constituent codes parallel concatenated schemes employing two convolutional codes as constituent codes in connection with an iterative decoding algorithm of complexity comparable to that of the constituent codes have been previously shown to yield remarkable coding gains close to theoretical limits they have been named and are known as turbo codes we propose a method to evaluate an upper bound to the bit error probability of a parallel concatenated coding scheme averaged over all interleavers of a given length the analytical bounding technique is then used to shed some light on some crucial questions which have been floating around in the communications community since the proposal of turbo codes

coherence on fractals versus pointwise convergence for the schrodinger equation we consider carleson s problem regarding convergence for the schrodinger equation in dimensions d ge 2 we show that if the solution converges almost everywhere with respect to alpha hausdorff measure to its initial datum as time tends to zero for all data h s mathbb r d then s ge frac d 2 d 2 d 1 alpha this strengthens and generalises results of bourgain and dahlberg kenig

the lie point symmetry generators admitted by systems of linear differential equations computing the lie point symmetries of systems of linear differential equations can be prohibitively difficult for homogeneous systems in kovalevskaya form of order two or higher this paper proves