1,721,013 research outputs found
On asymptotic stability of moving ground states of the nonlinear Schr\"odinger equation
No full textWe extend to the case of moving solitons, the result on asymptotic stability of ground states of the NLS obtained by the author in an earlier paper
On instability of excited states of the nonlinear Schrödinger equation
No full textWe introduce a new notion of linear stability for standing waves of the nonlinear Schrödinger equation (NLS) which requires not only that the spectrum of the linearization be real, but also that the generalized kernel be not degenerate and that the signature of all the positive eigenvalues be positive. We prove that excited states of the NLS are not linearly stable in this more restrictive sense. We then give a partial proof that this more restrictive notion of linear stability is a necessary condition to have orbital stability
Asymptotic stability of the ground states of the nonlinear Schr"odinger equation
No full textDiamo una panoramica sulla stabilita asintotica degli stati fondamentali di equazioni di Schroedinger nonlinear
estimates for averaging operators along curves with two sided k fold singularities
No full textWe prove optimal regularity in L^2 for a special class of Fourier integral operators with k folds singularities. We give also a new proof of the classical result for simple folds due to Melrose and Taylo
Stabilization of solutions to nonlinear Schr"odinger equations
No full textwe prove asymptotic stability of ground states of the NLS without internal mode
Orbitally but not asymptotically stable ground states for the discrete NLS.
No full textWe consider examples of discrete nonlinear Schr\"odinger equations in Z admitting ground states which are orbitally but not asymptotically stable in l ^2(Z ). The ground states contain internal modes which decouple from the continuous modes. The absence of leaking of energy from discrete to continues modes leads to an almost conservation and perpetual oscillation of the discrete modes. This is quite different from what is known for nonlinear Schr\"odinger equations in R ^d. To achieve our goal we prove a Siegel normal form theorem, prove dispersive estimates for the linearized operators and prove some nonlinear estimate
On the local existence for the Maxwell Klein Gordon system in
No full textWe prove low regularity local existence of solutions of the Maxwell Klein Gordon system in $ R ^{3+1}
On dispersion for Klein Gordon Equation with periodic potential in 1D
Full text linkBy exploiting estimates on Bloch functions obtained in a previous paper, we prove decay estimates for Klein Gordon equations with a time independent potential periodic in space in 1D and with generic mas
On asymptotic stability in energy space of ground states of NLS in 1D
No full textWe transpose work by T.Mizumachi to prove smoothing estimates for dispersive solutions of the linearization at a ground state of a Nonlinear Schr\"odinger 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 & Mizumachi for dimensions $\ge 3
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