The N-Soliton Interactions, Complex Toda Chain and Stable Propagation of NLS Soliton Trains

1999 ◽  
pp. 219-226
Author(s):  
V. S. Gerdjikov ◽  
E. G. Evstatiev ◽  
D. J. Kaup ◽  
G. L. Diankov ◽  
I. M. Uzunov
Keyword(s):  
Toda Chain ◽  
Soliton Interactions ◽  
Stable Propagation ◽  
Complex Toda Chain

Generalized perturbed complex Toda chain for Manakov system and exact solutions of Bose–Einstein mixtures

2009 ◽  
Vol 80 (1) ◽  
pp. 112-119 ◽  
Author(s):  
V.S. Gerdjikov ◽  
N.A. Kostov ◽  
E.V. Doktorov ◽  
N.P. Matsuka
Keyword(s):  
Exact Solutions ◽  
Toda Chain ◽  
Bose Einstein ◽  
Complex Toda Chain

scholarly journals Adiabatic interaction ofNultrashort solitons: Universality of the complex Toda chain model

2001 ◽  
Vol 64 (5) ◽  
Author(s):  
V. S. Gerdjikov ◽  
E. V. Doktorov ◽  
J. Yang
Keyword(s):  
Toda Chain ◽  
Chain Model ◽  
Complex Toda Chain

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

2007 ◽  
Vol 151 (3) ◽  
pp. 762-773 ◽  
Author(s):  
V. S. Gerdjikov ◽  
E. V. Doktorov ◽  
N. P. Matsuka
Keyword(s):  
Toda Chain ◽  
Generalized Complex ◽  
Complex Toda Chain

scholarly journals On Asymptotic Dynamical Regimes of Manakov N-soliton Trains in Adiabatic Approximation

2020 ◽  
pp. 678-693
Author(s):  
Vladimir S. Gerdjikov ◽  
Michail D. Todorov
Keyword(s):  
Adiabatic Approximation ◽  
Dynamical Behavior ◽  
Toda Chain ◽  
Bound State ◽  
Explicit Description ◽  
Asymptotic Regime ◽  
Asymptotic Velocity ◽  
Dynamical Regimes ◽  
State Regime ◽  
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

Laser Glittering in the Relatively Stable Propagation Layer Near the Sea Surface

1991 ◽  
Author(s):  
Le Shixhiao
Keyword(s):  
Sea Surface ◽  
Stable Propagation

scholarly journals Generalized Gibbs Ensembles of the Classical Toda Chain

2019 ◽  
Vol 180 (1-6) ◽  
pp. 4-22 ◽  
Author(s):  
Herbert Spohn
Keyword(s):  
Toda Chain
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