Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2003-09-20
Nonlinear Sciences
Pattern Formation and Solitons
Phys. Rev. E, in press
Scientific paper
10.1103/PhysRevE.68.056603
We examine collisions between identical solitons in a weakly perturbed Ablowitz-Ladik (AL) model, augmented by either onsite cubic nonlinearity (which corresponds to the Salerno model, and may be realized as an array of strongly overlapping nonlinear optical waveguides), or a quintic perturbation, or both. Complex dependences of the outcomes of the collisions on the initial phase difference between the solitons and location of the collision point are observed. Large changes of amplitudes and velocities of the colliding solitons are generated by weak perturbations, showing that the elasticity of soliton collisions in the AL model is fragile (for instance, the Salerno's perturbation with the relative strength of 0.08 can give rise to a change of the solitons' amplitudes by a factor exceeding 2). Exact and approximate conservation laws in the perturbed system are examined, with a conclusion that the small perturbations very weakly affect the norm and energy conservation, but completely destroy the conservation of the lattice momentum, which is explained by the absence of the translational symmetry in generic nonintegrable lattice models. Data collected for a very large number of collisions correlate with this conclusion. Asymmetry of the collisions (which is explained by the dependence on the location of the central point of the collision relative to the lattice, and on the phase difference between the solitons) is investigated too, showing that the nonintegrability-induced effects grow almost linearly with the perturbation strength. Different perturbations (cubic and quintic ones) produce virtually identical collision-induced effects, which makes it possible to compensate them, thus finding a special perturbed system with almost elastic soliton collisions.
Dmitriev Sergey V.
Frantzeskakis Dimitri J.
Kevrekidis Panagiotis G.
Malomed Boris A.
No associations
LandOfFree
Two-soliton collisions in a near-integrable lattice system does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Two-soliton collisions in a near-integrable lattice system, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Two-soliton collisions in a near-integrable lattice system will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-276196