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Classical Conservative Properties of Five Difference Schemes for Coupled Klein-Gordon-Schr ?dinger Equations
Klein-Gordon-Schr膐dinger equations difference schemes conservation
2012/8/7
In this paper we compare the classical conservative properties of 痸e
di甧rence schemes applied to the coupled Klein-Gordon-Schr膐dinger equations in the
quantum physics, and investigate the numerical ...
Localizing Estimates of the Support of Solutions of some Nonlinear Schrödinger Equations - The Stationary Case
nonlinear Schrodinger equation compact support energy method
2011/1/19
The main goal of this paper is to study the nature of the support of the solution of suitable
nonlinear Schrodinger equations mainly the compactness of the support and its spatial localization.
Numerical Continuation of resonances and bound states in coupled channel Schrödinger equations
Resonances Numerical Continuation Coupled Channels Schr¨odinger equation
2011/1/17
In this contribution, we introduce numerical continuation methods and bifurcation theory, techniques which find their roots in the study of dynamical systems,to the problem of tracing the parameter de...
Asymptotic stability of small solitary waves for nonlinear Schrödinger equations with electromagnetic potential in $ \mathbb{R}^3$
Asymptotic stability of small solitary waves nonlinear Schrö dinger equations electromagnetic potential $ \mathbb{R}^3$
2011/1/17
We consider the nonlinear magnetic Schr¨odinger equation for u : R3 × R → C,iut = (i∇ + A)2u + V u + g(u), u(x, 0) = u0(x),where A : R3 → R3 is the magnetic potential, V : R3 → R is the electric...
Transverse instability for periodic waves of KP-I and Schrödinger equations
transverse instability periodic traveling waves KP-I equation Schr¨odinger equation
2011/1/21
We consider the quadratic and cubic KP - I and NLS models in 1+2 dimensions with periodic boundary conditions. We show that the spatially periodic travelling waves (with period
K) in the form u(t, x,...
Strichartz estimates for partially periodic solutions to Schrödinger equations in 4d and applications
Schrö dinger equations 4d applications
2010/11/9
We consider the energy critical nonlinear Schr\"odinger equation on periodic domains of the form R^m x T^{4-m} with m=0,1,2,3. Assuming that a certain L^4 Strichartz estimate holds for solutions to t...
On the Cauchy Problem for nonlinear Schrödinger equations with rotation
Nonlinear Schr¨odinger equation Bose-Einstein condensation rotation
2010/12/9
We consider the Cauchy problem for (energy-subcritical) nonlinear Schr¨odinger equations with sub-quadratic external potentials and an additional angular momentum rotation term. This equation is a wel...
Positive solutions of Schrödinger equations and fine regularity of boundary points
Schrö dinger equations fine regularity of boundary points
2010/12/9
Given a Lipschitz domain in RN and a nonnegative potential V in such that V (x) d(x.
Solutions to nonlinear Schrödinger equations with singular electromagnetic potential and critical exponent
nonlinear Schrö dinger equations singular electromagnetic potential critical exponent
2010/12/8
We investigate existence and qualitative behaviour of solutions to nonlinear Schr¨odinger equations with critical exponent and singular electromagnetic potentials. We are concerned with with magnetic ...
On the Global Existence and Blowup Phenomena of Schrödinger Equations with Multiple Nonlinearities
Nonlinear Schr¨odinger equation Global existence Blow up in Nonlinear Schr¨odinger equation Global existence
2010/11/29
In this paper, we consider the global existence and blowup phenomena of the following Cauchy problem−iut = u − V (x)u + f(x, |u|2)u + (W ⋆ |u|2)u, x ∈ RN, t > 0,u(x, 0) = u0(x), x ...
Nonlinear instability of linearly unstable standing waves for nonlinear Schrödinger equations
Nonlinear instability linearly unstable standing waves nonlinear Schrö dinger equations
2010/12/13
We study the instability of standing waves for nonlinear Schr¨odinger equations. Under a general assumption on nonlinearity, we prove that linear instability implies orbital instability in any dimensi...
Probabilistic methods for discrete nonlinear Schrödinger equations
Nonlinear Schrodinger equation invariant measure discrete breather exactly solvable model
2010/12/14
Using techniques from probability theory, we show that the thermodynamics of the focusing cubic discrete nonlinear Schrodinger equation (NLS) are exactly solvable in dimensions three and higher.A num...
STANDING WAVES OF THE DISCRETE NONLINEAR SCHR ¨O DINGER EQUATIONS WITH GROWING POTENTIALS
discrete nonlinear Schr¨odinger equation standing wave variation methods Nehari manifold
2008/11/26
In this paper we investigate the existence of nontrivial standing wave solution of the
discrete nonlinear Schr¨odinger equation with the growing potential at infinity. Firstly
we derive a discrete v...
Fundamental Solution Global in Time for a Class of Schrödinger Equations with Time-Dependent Potentials
Schrö dinger equation fundamental solution Fourier integral operators long-range potentials scattering theory
2008/11/25
Fundamental solution for a Schrödinger equation with a time-dependent potential of
long-range type is constructed. The solution is given as a Fourier integral operator with
a symbol uniformly b...