DYNAMICAL CHARACTER FOR A PERTURBED COUPLED NONLINEAR SCHRDINGER SYSTEM

Introduction WeconsidertheperturbedcouplednonlinearSchr dingerequations(CNLS)iq1t=q1xx 2[|q1|2 |q2|2-ω2]q1 iε(^D1q1-r1),iq2t=q2xx 2[|q1|2 |q2|2-ω2]q2 iε(^D2q2-r2),(1)whereqjis2πperiodicandeveninx.rjisconstant,^Djisboundeddissipativeoperatorand assumedtotaketheform^Djqj=-αjqj βj^Bqj,(2)αjandβjarepositiveconstants,j=1,2.^BisaFouriertruncationofLaplaceoperator xx,i.e.,^Bcos(kx)=-k2cos(kx),k0isasmallperturbation parameter.Th…     

MODEL OF CENTRIFUGAL EFFECT AND ATTITUDE MANEUVER STABILITY OF A COUPLED RIGID-FLEXIBLE SYSTEM

IntroductionThedynamicandcontrolofcoupledrigid_flexiblesystemisaleading_edgeresearchsubjectthathasdrawnextensiveattentionfromtheacademiccommunityintheworld[1].TheresearchconductedbyKaneetal.in 1 987[2 ]suggestedthat,thetraditionalmodelapplyingstructuraldynamicsassumptionaboutelasticdeformationindiscriminately[3,4 ],ineffect,hasneglectedtheso_called“dynamicstiffening”effectresultedfromcoupledrigid_flexiblesystem .Therefore ,itisofparticularimportancetoresearchtheactionofcoupledrigid_flexibles…     

CONCENTRATION OF COUPLED CUBIC NONLINEAR SCHRODINGER EQUATIONS

A coupled nonlinear Schrodinger equations is considered in 2-D space. Based upon the conservation of mass and energy, local identities is established by the study of the limit behavior of the solutions, and L^2-concentration for the blow-up solutions with radially symmetry is obtained.     

The maximum dissipative extension of Schrödinger operator

In the present paper we study the maximum dissipative extension of Schrodingeroperator.introduce the generalized indefinite metvic space and get the representation ofmaximum dissipative extension of Schrodinger operator in natural boundary space.make preparation for the further study longtime chaotic behaxior of infinite dimensiondynamics system in nonlinear Schrodinger equation.     

Global attractor for Klein-Gordon-Schroedinger lattice system

We considered the longtime behavior of solutions of a coupled lattice dynamical system of Klein-Gordon-Schroedinger equation （KGS lattice system）. We first proved the existence of a global attractor for the system considered here by introducing an equivalent norm and using ＂End Tails＂ of solutions. Then we estimated the upper bound of the Kolmogorov delta-entropy of the global attractor by applying element decomposition and the covering property of a polyhedron by balls of radii delta in the finite dimensional space. Finally, we presented an approximation to the global attractor by the global attractors of finite-dimensional ordinary differential systems.     

Boundary value problem for a singularly perturbed nonlinear system

I.Intr0ducti0n'Manyresultshavebeeng0tinstudyingthesingu1arperturbation0fboundaryvalueproblemfornonlinearsystemeg#=j(t,g,y',8)(l.l)bythemethodandthetechniqueofdiagonalizationl'~'l.Thepapersarebasedonsucha.conditionthattheeigenvaluesofJacobimatrixlu'offwit…     

Orbital stability of periodic waves for the nonlinear Schrödinger equation

The nonlinear Schr?dinger equation has several families of quasi-periodic traveling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its phase over a period (Floquet exponent). In the defocusing case, we show that these travelling waves are orbitally stable within the class of solutions having the same period and the same Floquet exponent. This generalizes a previous work (Gallay and Haragus, J. Diff. Equations, 2007) where only small amplitude solutions were considered. A similar result is obtained in the focusing case, under a non-degeneracy condition which can be checked numerically. The proof relies on the general approach to orbital stability as developed by Grillakis, Shatah, and Strauss, and requires a detailed analysis of the Hamiltonian system satisfied by the wave profile.     

Characteristic fractional step finite difference method for nonlinear section coupled system

For the section coupled system of multilayer dynamics of fluids in porous media, a parallel scheme modified by the characteristic finite difference fractional steps is proposed for a complete point set consisting of coarse and fine partitions. Some tech- niques, such as calculus of variations, energy method, twofold-quadratic interpolation of product type, multiplicative commutation law of difference operators, decomposition of high order difference operators, and prior estimates, are used in theoretical analysis. Optimal order estimates in 12 norm are derived to show accuracy of the second order approximation solutions. These methods have been used to simulate the problems of migration-accumulation of oil resources.     

Initial-boundary value problem of one class of nonlinear Schrödinger equations described in molecular crystals

In this paper, we study the initiial-boundary value problem of one class of nonlinear Schrodinger equations described in molecular crystals. Furthermore, the existence of the global solution is obtained by means of interpolation inequality and a priori estimation.     

Note on the modified nonlinear Schrödinger equation for deep water waves

It is shown that Zakharov's integral equation yields the modified Schrödinger equation for the particular case of a narrow spectrum.     

Global solution for coupled nonlinear Klein-Gordon system

The globed solution for a coupled nonlinear Klein-Gordon system in two-dimensional space was studied. First, a sharp threshold of blowup and global existence for the system was obtained by constructing a type of cross-constrained variational problem and establishing so-called cross-invariant manifolds of the evolution flow. Then the result of how small the initial data for which the solution exists globally was proved by using the scaling argument.