Geodesic
On asymptotic dynamical regimes of Manakov $N$-soliton trains in adiabatic approximation
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 6, pp. 678-693

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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.
Keywords: Manakov model, adiabatic approximations complex Toda chain.
Mots-clés : soliton interactions 
@article{JSFU_2020_13_6_a2,
     author = {Vladimir S. Gerdjikov and Michail D. Todorov},
     title = {On asymptotic dynamical regimes of {Manakov} $N$-soliton trains in adiabatic approximation},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {678--693},
     publisher = {mathdoc},
     volume = {13},
     number = {6},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_6_a2/}
}
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Vladimir S. Gerdjikov; Michail D. Todorov. On asymptotic dynamical regimes of Manakov $N$-soliton trains in adiabatic approximation. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 6, pp. 678-693. http://geodesic.mathdoc.fr/item/JSFU_2020_13_6_a2/