V. S. Gerdjikov, E. V. Doktorov, N. P. Matsuka, “<nobr>$N$</nobr>-soliton train and generalized complex Toda chain for the Manakov system”, TMF, 2007, Volume 151, Number 3,Pages <nobr>391

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$N$-soliton train and generalized complex Toda chain for the Manakov system

V. S. Gerdjikov^a, E. V. Doktorov^b, N. P. Matsuka^c

^a Institute for Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences
^b B. I. Stepanov Institute of Physics, National Academy of Sciences of Belarus
^c Institute of Mathematics, National Academy of Sciences of the Republic of Belarus

Abstract: 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, vector soliton train.

DOI: 10.4213/tmf6054