17 citations · 17 across the 4 of their papers we have counts for
5 papers
Stability and instability analysis of resonance-induced nonlinear bound states
Jackson C. Turner, Michael I. Weinstein
We study the focusing one-dimensional cubic nonlinear Schrödinger / Gross--Pitaevskii equation (NLS-GP), where the potential of the underlying linear Schrödinger operator, $H_V=-\p…
Stability theory of flat band solitons in nonlinear wave systems
Cheng Shi, Ross Parker, Panayotis G. Kevrekides +1
We establish a sharp criterion for the stability of a class of compactly supported, homogeneous density``minimal compact solitons'' or MCS states, of the time-dependent discrete no…
Resonance-induced nonlinear bound states
Jackson C. Turner, Michael I. Weinstein
We study nonlinear bound states -- time-harmonic and spatially decaying () solutions -- of the nonlinear Schrödinger / Gross--Pitaevskii equations (NLS/GP) with a compactly su…
Stability of traveling waves in a nonlinear hyperbolic system approximating a dimer array of oscillators
Huaiyu Li, Andrew Hofstrand, Michael I. Weinstein
We study a semilinear hyperbolic system of PDEs which arises as a continuum approximation of the discrete nonlinear dimer array model introduced by Hadad, Vitelli and Alu (HVA) in…
Metastability of Breather Modes of Time-Dependent Potentials
P. D. Miller, A. Soffer, M. I. Weinstein
We study the solutions of linear Schroedinger equations in which the potential energy is a periodic function of time and is sufficiently localized in space. We consider the potenti…