dcca cross correlation coefficient quantifying level of cross correlation abstract in this paper a new coefficient is proposed with the objective of quantifying the level of cross correlation between nonstationary time series this cross correlation coefficient is defined in terms of the dfa method and the dcca method the implementation of this cross correlation coefficient will be illustrated with selected time series

stability of standing waves for nls with perturbed lame potential abstract we perturb a linear schrodinger equation with lame potential with a small positive or negative potential the new perturbed operator has one or more eigenvalues at most one in each spectral gap we then add a nonlinear term and study the stability of the corresponding nonlinear stationary waves

detrending moving average algorithm for multifractals the detrending moving average dma algorithm is a widely used technique to quantify the long term correlations of nonstationary time series and the long range correlations of fractal surfaces which contains a parameter ensuremath theta determining the position of the detrending window we develop multifractal detrending moving average mfdma algorithms for the analysis of one dimensional multifractal measures and higher dimensional multifractals which is a generalization of the dma method the performance of the one dimensional and two dimensional mfdma methods is investigated using synthetic multifractal measures with analytical solutions for backward ensuremath theta 0 centered ensuremath theta 0 5 and forward ensuremath theta 1 detrending windows we find that the estimated multifractal scaling exponent ensuremath tau q and the singularity spectrum f ensuremath alpha are in good agreement with the theoretical values in addition the backward mfdma method has the best performance which provides the most accurate estimates of the scaling exponents with lowest error bars while the centered mfdma method has the worse performance it is found that the backward mfdma algorithm also outperforms the multifractal detrended fluctuation analysis the one dimensional backward mfdma method is applied to analyzing the time series of shanghai stock exchange composite index and its multifractal nature is confirmed

stability of solitary waves for nonlinear schrodinger equations with inhomogeneous nonlinearities we show that the ground state solitary waves of the critical nonlinear schrodinger equation i t t r v 4 d 0 in dimension d 2 are orbitally stable as 0i f v 0 v 4 0 g d v 0 2 where gd is a constant that depends only on d 2002 elsevier science b v all rights reserved

lp lp estimates for the schrodinger equation on the line and inverse scattering for the nonlinear schrodinger equation with a potential abstract in this paper i prove a l p l p estimate for the solutions to the one dimensional schrodinger equation with a potential in l 1 where in the generic case 3 2 and in the exceptional case i e when there is a half bound state of zero energy 5 2 i use this estimate to construct the scattering operator for the nonlinear schrodinger equation with a potential i prove moreover that the low energy limit of the scattering operator uniquely determines the potential and the coupling constant of the nonlinearity using a method that allows as well for the reconstruction of the potential and of the nonlinearity

nonlinear instability of half solitons on star graphs abstract we consider a half soliton stationary state of the nonlinear schrodinger equation with the power nonlinearity on a star graph consisting of n edges and a single vertex for the subcritical power nonlinearity the half soliton state is a degenerate critical point of the action functional under the mass constraint such that the second variation is nonnegative by using normal forms we prove that the degenerate critical point is a saddle point for which the small perturbations to the half soliton state grow slowly in time resulting in the nonlinear instability of the half soliton state the result holds for any n 3 and arbitrary subcritical power nonlinearity it gives a precise dynamical characterization of the previous result of adami et al 2012 2 where the half soliton state was shown to be a saddle point of the action functional under the mass constraint for n 3 and for cubic nonlinearity

asymptotic stability of small gap solitons in nonlinear dirac equations we prove dispersive decay estimates for the one dimensional dirac operator and use them to prove asymptotic stability of small gap solitons in the nonlinear dirac equations with quintic and higher order nonlinear terms

wobbling kinks in ϕ 4 theory we present a uniform asymptotic expansion of the wobbling kink to any order in the amplitude of the wobbling mode the long range behavior of the radiation is described by matching the asymptotic expansions in the far field and near the core of the kink the complex amplitude of the wobbling mode is shown to obey a simple ordinary differential equation with nonlinear damping we confirm the t ensuremath 1 2 decay law for the amplitude which was previously obtained on the basis of energy considerations

global dynamics above the ground state energy for the one dimensional nlkg equation in this paper we obtain a global characterization of the dynamics of even solutions to the one dimensional nonlinear klein gordon nlkg equation on the line with focusing nonlinearity u p 1 u p 5 provided their energy exceeds that of the ground state only sightly the method is the same as in the three dimensional case nakanishi and schlag in global dynamics above the ground state energy for the focusing nonlinear klein gordon equation preprint 2010 the major difference being in the construction of the center stable manifold the difficulty there lies with the weak dispersive decay of 1 dimensional nlkg in order to address this specific issue we establish local dispersive estimates for the perturbed linear klein gordon equation similar to those of mizumachi j math kyoto univ 48 3 471 497 2008 the essential ingredient for the latter class of estimates is the absence of a threshold resonance of the linearized operator

spectral stability of small amplitude solitary waves of the dirac equation with the soler type nonlinearity abstract we study the point spectrum of the linearization at a solitary wave solution x e i t to the nonlinear dirac equation in r n for all n 1 with the nonlinear term given by f known as the soler model we focus on the spectral stability that is the absence of eigenvalues with positive real part in the non relativistic limit m 0 in the case when f c 1 r 0 f o k for 0 with 0 k for n 1 we prove the spectral stability of small amplitude solitary waves m for the charge subcritical cases 2 n in particular 1 2 when n 1 and for the charge critical case 2 n with k 4 n an important part of the stability analysis is the proof of the absence of bifurcation of nonzero real part eigenvalues from the embedded threshold points at 2 m i our approach is based on constructing a new family of exact bi frequency solitary wave solutions in the soler model and on the analysis of the behavior of nonlinear eigenvalues characteristic roots of holomorphic operator valued functions

on asymptotic stability in energy space of ground states of nls in 1d abstract we transpose work by t mizumachi to prove smoothing estimates for dispersive solutions of the linearization at a ground state of a nonlinear schrodinger equation nls in 1d as an application we extend to dimension 1d a result on asymptotic stability of ground states of nls proved by cuccagna and mizumachi for dimensions 3

multichannel nonlinear scattering for nonintegrable equations ii the case of anisotropic potentials and data abstract the nonlinear scattering and stability results of soffer and weinstein comm math phys 1990 are extended to the case of anisotropic potentials and data the range of nonlinearities for which the theory is shown to be valid is also extended considerably

symmetry breaking bifurcation in the nonlinear schrodinger equation with symmetric potentials we consider the focusing attractive nonlinear schrodinger nls equation with an external symmetric potential which vanishes at infinity and supports a linear bound state we prove that the symmetric nonlinear ground states must undergo a symmetry breaking bifurcation if the potential has a non degenerate local maxima at zero under a generic assumption we show that the bifurcation is either a subcritical or supercritical pitchfork in the particular case of double well potentials with large separation the power of nonlinearity determines the subcritical or supercritical character of the bifurcation the results are obtained from a careful analysis of the spectral properties of the ground states at both small and large values for the corresponding eigenvalue parameter

are crude oil markets multifractal evidence from mf dfa and mf ssa perspectives abstract in this article we investigated the multifractality and its underlying formation mechanisms in international crude oil markets namely brent and wti which are the most important oil pricing benchmarks globally we attempt to find the answers to the following questions 1 are those different markets multifractal 2 what are the dynamical causes for multifractality in those markets if any to answer these questions we applied both multifractal detrended fluctuation analysis mf dfa and multifractal singular spectrum analysis mf ssa based on the partition function two widely used multifractality detecting methods we found that both markets exhibit multifractal properties by means of these methods furthermore in order to identify the underlying formation mechanisms of multifractal features we destroyed the underlying nonlinear temporal correlation by shuffling the original time series thus we identified that the causes of the multifractality are influenced mainly by a nonlinear temporal correlation mechanism instead of a non gaussian distribution at last by tracking the evolution of left and right half multifractal spectra we found that the dynamics of the large price fluctuations is significantly different from that of the small ones our main contribution is that we not only provided empirical evidence of the existence of multifractality in the markets but also the sources of multifractality and plausible explanations to current literature furthermore we investigated the different dynamical price behaviors influenced by large and small price fluctuations

invariant manifolds for a class of dispersive hamiltonian partial differential equations we construct an invariant manifold of periodic orbits for a class of non linear schrodinger equations using standard ideas of the theory of center manifolds we rederive the results of soffer and weinstein comm math phys 133 119 146 1997 j differential equations98 376 390 1992 on the large time asymptotics of small solutions scattering theory

instability of nonlinear bound states we establish a sharp instability theorem for the bound states of lowest energy of the nonlinear klein gordon equation utt u f u 0 and the nonlinear schrodinger equation iut u f u 0

stability theory of solitary waves in the presence of symmetry ii abstract consider an abstract hamiltonian system which is invariant under a group of operators we continue to study the effect of the group invariance on the stability of solitary waves applications are given to bound states and traveling wave solutions of nonlinear wave equations

maximal functions associated to filtrations abstract let t be a bounded linear or sublinear operator from lp y to lq x a maximal operator t f x supj t f yj x is associated to any sequence of subsets yj of y under the hypotheses that q p and the sets yj are nested we prove that t is also bounded classical theorems of menshov and zygmund are obtained as corollaries multilinear generalizations of this theorem are also established these results are motivated by applications to the spectral analysis of schrodinger operators

long range correlation and market segmentation in bond market abstract this paper investigates the long range auto correlations and cross correlations in bond market based on detrended moving average dma method empirical results present a clear evidence of long range persistence that exists in one year scale the degree of long range correlation related to maturities has an upward tendency with a peak in short term these findings confirm the expectations of fractal market hypothesis fmh furthermore we have developed a method based on a complex network to study the long range cross correlation structure and applied it to our data and found a clear pattern of market segmentation in the long run we also detected the nature of long range correlation in the sub period 2007 2012 and 2011 2016 the result from our research shows that long range auto correlations are decreasing in the recent years while long range cross correlations are strengthening

on asymptotic stability of moving ground states of the nonlinear schrodinger equation we extend to the case of moving solitons the result on asymptotic stability of ground states of the nls obtained by the author in cu1 for technical reasons we consider only smooth solutions the proof is similar to the earlier paper however now the flows required for the darboux theorem and the birkhoff normal forms instead of falling within the framework of standard theory of ode s are related to quasilinear hyperbolic symmetric systems it is also not obvious that darboux theorem can be applied since we need to compare two symplectic forms in a neighborhood of the ground states not in h r but rather in the space where also the variance is bounded but the nls does not preserve small neighborhoods of the ground states in

normal form for the symmetry breaking bifurcation in the nonlinear schrodinger equation abstract we derive and justify a normal form reduction of the nonlinear schrodinger equation for a general pitchfork bifurcation of the symmetric bound state that occurs in a double well symmetric potential we prove persistence of normal form dynamics for both supercritical and subcritical pitchfork bifurcations in the time dependent solutions of the nonlinear schrodinger equation over long but finite time intervals

an invariant set in energy space for supercritical nls in 1d we consider radial solutions of a mass supercritical monic nls and we prove the existence of a set which looks like a hypersurface in the space of finite energy functions invariant for the flow and formed by solutions which converge to ground states

stable manifolds for all monic supercritical focusing nonlinear schrodinger equations in one dimension keywords critical schrodinger equation stable manifolds modulation theory spectral theory klein gordon equations non linear schrodinger blow up rate standing waves nonintegrable equations invariant manifolds stability theory solitary waves ground states instability reference epfl article 155183doi 10 1090 s0894 0347 06 00524 8 record created on 2010 11 19 modified on 2017 05 12

lyapunov stability of ground states of nonlinear dispersive evolution equations on presente une nouvelle demonstration de la stabilite orbitale des solitons d etat fondamental de l equation de schrodinger non lineaire pour une grande classe de non linearites on demontre la stabilite de l onde solitaire pour l equation de korteweg de vries generalisee

center manifold for nonintegrable nonlinear schrodinger equations on the line in this paper we study the following nonlinear schrodinger equation on the line where f is real valued and it satisfies suitable conditions on regularity on growth as a function of u and on decay as x the generic potential v is real valued and it is chosen so that the spectrum of consists of one simple negative eigenvalue and absolutely continuous spectrum filling 0 the solutions to this equation have in general a localized and a dispersive component the nonlinear bound states that bifurcate from the zero solution at the energy of the eigenvalue of h define an invariant center manifold that consists of the orbits of time periodic localized solutions we prove that all small solutions approach a particular periodic orbit in the center manifold as t in general the periodic orbits are different for t our result implies also that the nonlinear bound states are asymptotically stable in the sense that each solution with initial data near a nonlinear bound state is asymptotic as t to the periodic orbits of nearby nonlinear bound states that are in general different for t

spectra of positive and negative energies in the linearized nls problem we study the spectrum of the linearized nls equation in three dimensions in association with the energy spectrum we prove that unstable eigenvalues of the linearized nls problem are related to negative eigenvalues of the energy spectrum while neutrally stable eigenvalues may have both positive and negative energies the nonsingular part of the neutrally stable essential spectrum is always related to the positive energy spectrum we derive bounds on the number of unstable eigenvalues of the linearized nls problem and study bifurcations of embedded eigenvalues of positive and negative energies we develop the l 2 scattering theory for the linearized nls operators and recover results of grillakis 5 with a fermi golden rule c

on asymptotic stability in energy space of ground states for nonlinear schrodinger equations we consider nonlinear schrodinger equations iu t delta u beta u 2 u 0 text for t x in mathbb r times mathbb r d where d 3 and is smooth we prove that symmetric finite energy solutions close to orbitally stable ground states converge to a sum of a ground state and a dispersive wave as t assuming the so called the fermi golden rule fgr hypothesis we improve the sign condition required in a recent paper by gang zhou and i m sigal

asymptotic dynamics of nonlinear schrodinger equations with many bound states abstract we consider a nonlinear schrodinger equation with a bounded localized potential in r 3 the linear hamiltonian is assumed to have three or more bound states with the eigenvalues satisfying some resonance conditions suppose that the initial data is localized and small of order n in h1 and that its ground state component is larger than n3 e with e 0 small we prove that the solution will converge locally to a nonlinear ground state as the time tends to infinity

asymptotic dynamics of nonlinear schrodinger equations resonance dominated and dispersion dominated solutions we consider a linear schrodinger equation with a nonlinear perturbation in r 3 assume that the linear hamiltonian has exactly two bound states and its eigenvalues satisfy some resonance condition we prove that if the initial data is sufficiently small and is near a nonlinear ground state then the solution approaches to certain nonlinear ground state as the time tends to infinity furthermore the difference between the wave function solving the nonlinear schrodinger equation and its asymptotic profile can have two different types of decay the resonancedominated solutions decay as t 1 2 or the dispersion dominated solutions decay at least like t 3 2 c 2002 john wiley sons inc

on the spectral theory and dispersive estimates for a discrete schrodinger equation in one dimension based on the recent work komech et al dispersive estimates for 1d discrete schrodinger and klein gordon equations appl anal 85 1487 2006 for compact potentials we develop the spectral theory for the one dimensional discrete schrodinger operator h v n 1 n 1 2 n vn n we show that under appropriate decay conditions on the general potential and a nonresonance condition at the spectral edges the spectrum of h consists of finitely many eigenvalues of finite multiplicities and the essential absolutely continuous spectrum while the resolvent satisfies the limiting absorption principle and the puiseux expansions near the edges these properties imply the dispersive estimates eithpa c h l 2 l 2 t 3 2 for any fixed 52 and any t 0 where pa c h denotes the spectral projection to the absolutely continuous spectrum of h in addition based on the scattering theory for the discrete jost solutions and the previous results by stefanov and kevrekidis asymptotic behaviour of small