Soliton chaos in the nonlinear Schroedinger equation with spatially periodic perturbations

Journal Article · Tue Sep 15 04:00:00 EDT 1992 · Physical Review A. General Physics; (United States)

DOI:https://doi.org/10.1103/PhysRevA.46.R2973· OSTI ID:7262178

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)

We perturb the one-dimensional nonlinear Schroedinger equation with a time-independent spatially periodic potential with a period large compared to the spatial width of solitons present in the system. A collective-coordinate approximation maps the system to a nonintegrable many-particle dynamics with an effective Hamiltonian, which we derive under the assumption that we can neglect three-soliton collisions as well as two-soliton collisions with vanishing relative velocity. We give an estimate for the power radiated by a single soliton in the presence of the perturbation and show that radiative effects can be neglected for perturbations with sufficiently small amplitude and large spatial period. We show that the nonintegrability of this perturbed nonlinear Schroedinger equation manifests itself already in the two-soliton sector. We use the effective many-particle Hamiltonian to investigate soliton depinning. The effective Hamiltonian results are compared with numerical simulations of the full perturbed equation.

• OSTI ID: 7262178
• Journal Information: Physical Review A. General Physics; (United States), Journal Name: Physical Review A. General Physics; (United States) Vol. 46:6; ISSN 1050-2947; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

661100* -- Classical & Quantum Mechanics-- (1992-)
665000 -- Physics of Condensed Matter-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
COLLECTIVE MODEL
DIFFERENTIAL EQUATIONS
EQUATIONS
MANY-BODY PROBLEM
MAPPING
MATHEMATICAL MODELS
NONLINEAR PROBLEMS
NUCLEAR MODELS
PARTIAL DIFFERENTIAL EQUATIONS
QUASI PARTICLES
SCATTERING
SCHROEDINGER EQUATION
SOLITONS
WAVE EQUATIONS