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Nonlinear Schrödinger equations and sharp interpolation estimates

- M. Weinstein
- Mathematics
- 1 December 1983

AbstractA sharp sufficient condition for global existence is obtained for the nonlinear Schrödinger equation
$$\begin{array}{*{20}c} {(NLS)} & {2i\phi _t + \Delta \phi + \left| \phi \right|^{2\sigma… Expand

Modulational Stability of Ground States of Nonlinear Schrödinger Equations

- M. Weinstein
- Physics, Mathematics
- 1 May 1985

The modulational stability of ground state solitary wave solutions of nonlinear Schrodinger equations relative to perturbations in the equation and initial data is studied. In the “subcritical case”… Expand

Lyapunov stability of ground states of nonlinear dispersive evolution equations

- M. Weinstein
- Mathematics
- 1986

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… Expand

Dispersion of small amplitude solutions of the generalized Korteweg-de Vries equation

- F. M. Christ, M. Weinstein
- Mathematics
- 15 August 1991

Multichannel nonlinear scattering for nonintegrable equations

- A. Soffer, M. Weinstein
- Mathematics
- 1 September 1990

We consider a class of nonlinear Schrödinger equations (conservative and dispersive systems) with localized and dispersive solutions. We obtain a class of initial conditions, for which the asymptotic… Expand

Eigenvalues, and instabilities of solitary waves

- R. Pego, M. Weinstein
- MathematicsPhilosophical Transactions of the Royal Society…
- 15 July 1992

We study a type of ‘eigenvalue’ problem for systems of linear ordinary differential equations with asymptotically constant coefficients by using the analytic function D(λ) introduced by J. W. Evans… Expand

Asymptotic stability of solitary waves

- R. Pego, M. Weinstein
- Mathematics
- 1 August 1994

AbstractWe show that the family of solitary waves (1-solitons) of the Korteweg-de Vries equation
$$\partial _t u + u\partial _x u + \partial _x^3 u = 0 ,$$
is asymptotically stable. Our methods also… Expand

Resonances, radiation damping and instabilitym in Hamiltonian nonlinear wave equations

- A. Soffer, M. Weinstein
- Physics, Mathematics
- 29 June 1998

Abstract. We consider a class of nonlinear Klein-Gordon equations which are Hamiltonian and are perturbations of linear dispersive equations. The unperturbed dynamical system has a bound state, a… Expand

Existence and dynamic stability of solitary wave solutions of equations arising in long wave propagation

- M. Weinstein
- Mathematics
- 1987

We obtain conditions for the nonlinear stability (Theorem 5.1) of solitary waves fro two classes of nonlinear dispersive equations which arise in the mathematical description of long wave… Expand

On the structure and formation of singularities in solutions to nonlinear dispersive evolution equations

- M. Weinstein
- Mathematics
- 1986

On etudie le probleme aux valeurs initiales pour l'equation de Schrodinger non lineaire iΦ t +ΔΦ+|Φ| 2 σΦ=o, Φ:R x N ∈R t + →C, Φ(x,o)=Φ o (x)∈H 1 pour le cas critique σ=2/N

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