Length-scale competition for the one-dimensional nonlinear Schroedinger equation with spatially periodic potentials

Journal Article · Mon Feb 01 04:00:00 EST 1993 · Physical Review E; (United States)

DOI:https://doi.org/10.1103/PhysRevE.47.1375· OSTI ID:6994466

Scharf, R; Bishop, A R ^[1]

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1. Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

The effect of spatially periodic on-site potentials on solitons of the (1+1)-dimensional nonlinear Schroedinger equation depends not only on the amplitude of the perturbation but also on two length ratios---between the wavelength of the potential and either the spatial width of the soliton or its phase-modulation wavelength. For solitons which are slowly moving or at rest, only the first ratio is important: Solitons which are narrow compared to the wavelength of the potential move like particles in an effective potential; wide solitons move like renormalized'' particles; and for competing length scales, solitons are easily destabilized by the perturbation and break up into smaller localized excitations and radiation. For initially rapidly moving solitions in short-wavelength potentials, a different resonance effect is described which can inhibit soliton propagation. Away from this resonance the solitons can move in a dressed'' form radiating very slowly. Furthermore, it is shown numerically that two such dressed'' solitons reemerge after collision, essentially unchanged. We also comment on the structural stability of completely integrable dynamics under spatially periodic perturbations. Finally, we remark on the relevance of our results for the dynamical behavior of large polarons and bipolarons in disordered ionic lattices.

• OSTI ID: 6994466
• Journal Information: Physical Review E; (United States), Journal Name: Physical Review E; (United States) Vol. 47:2; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFERENTIAL EQUATIONS
ENERGY
EQUATIONS
NONLINEAR PROBLEMS
ONE-DIMENSIONAL CALCULATIONS
PARTIAL DIFFERENTIAL EQUATIONS
POLARONS
POTENTIAL ENERGY
QUASI PARTICLES
SCHROEDINGER EQUATION
SOLITONS
WAVE EQUATIONS
WAVE PROPAGATION