Physical Review Letters · 1994 · 116 citations · 16 references
Natural SciencesMathematicsPhysicsCondensed Matter PhysicsDynamical SystemsQuantum MechanicsDiscrete Dynamical SystemsDissipative SystemsNonlinear DynamicsNonlinear Wave DynamicsSchrödinger EquationStability TheoryDiscrete Nonlinear SystemsLocalized StatesSolitary WavesSoliton TheorySolitonsStability CriterionUnstable Region
An analytical stability criterion for discrete solitons is presented. Its evaluation proves that discreteness reduces (in comparison with the continuum results) the critical nonlinearity parameter (which separates stable and unstable regimes). Unstable discrete solitons may "collapse" into the more stable intrinsically localized states. The theory applies to a discrete nonlinear Schr\"odinger equation, but can be generalized to other systems.
16
Intrinsic Localized Modes in Anharmonic Crystals
A. J. Sievers, Sachio Takeno · Physical Review Letters · 1988 · 1.3K citations
A Nonlinear Difference Scheme and Inverse Scattering
Mark J. Ablowitz, J. F. Ladik · Studies in Applied Mathematics · 1976 · 517 citations