Journal of Siberian Federal University. Mathematics & Physics / On Asymptotic Dynamical Regimes of Manakov N-soliton Trains in Adiabatic Approximation

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Journal of Siberian Federal University. Mathematics & Physics. 2020 13 (6)
Gerdjikov, Vladimir S.; Todorov, Michail D.
Contact information
Gerdjikov, Vladimir S.: National Research Nuclear University MEPHI Moscow, Russian Federation; Institute of Mathematics and Informatics Bulgarian Academy of Sciences Sofia, Bulgaria; Institute for Advanced Physical Studies, New Bulgarian University Sofia, Bulgaria; ; OCRID: 0000-0002-1058-6565; Todorov, Michail D.: San Diego State University San Diego, CA, USA; Technical University of Sofia Sofia, Bulgaria; OCRID: 0000-0002-4019-5880
Manakov model; soliton interactions; adiabatic approximations complex Toda chain

We analyze the dynamical behavior of the N-soliton train in the adiabatic approximation of the Manakov model. The evolution of Manakov N-soliton trains is described by the complex Toda chain (CTC) which is a completely integrable dynamical model. Calculating the eigenvalues of its Lax matrix allows us to determine the asymptotic velocity of each soliton. So we describe sets of soliton parameters that ensure one of the two main types of asymptotic regimes: the bound state regime (BSR) and the free asymptotic regime (FAR). In particular we find explicit description of special symmetric configurations of N solitons that ensure BSR and FAR. We find excellent matches between the trajectories of the solitons predicted by CTC with the ones calculated numerically from the Manakov system for wide classes of soliton parameters. This confirms the validity of our model

Paper at repository of SibFU