Geodesic
$N$-soliton train and generalized complex Toda chain for the~Manakov system
Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 3, pp. 391-404

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We analyze the dynamical behavior of the $N$-soliton train of the Manakov system and of the vector NLS equation in the adiabatic approximation. We prove that the dynamics of the $N$-soliton train in both cases are described by a generalized version of the complex Toda chain model. This fact can be used to predict the asymptotic regimes of the $N$-soliton train provided the initial soliton parameters are given.
Keywords: complex Toda chain, Manakov model, adiabatic dynamics
Mots-clés : vector soliton train. 
@article{TMF_2007_151_3_a6,
     author = {V. S. Gerdjikov and E. V. Doktorov and N. P. Matsuka},
     title = {$N$-soliton train and generalized complex {Toda} chain for {the~Manakov} system},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {391--404},
     publisher = {mathdoc},
     volume = {151},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_151_3_a6/}
}
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V. S. Gerdjikov; E. V. Doktorov; N. P. Matsuka. $N$-soliton train and generalized complex Toda chain for the~Manakov system. Teoretičeskaâ i matematičeskaâ fizika, Tome 151 (2007) no. 3, pp. 391-404. http://geodesic.mathdoc.fr/item/TMF_2007_151_3_a6/