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

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

Chaotic and Hyperchaotic Dynamics of a Modified Murali–Lakshmanan–Chua Circuit

2019 ◽  
Vol 14 (5) ◽  
Author(s):  
I. Manimehan ◽  
M. Paul Asir ◽  
P. Philominathan
Keyword(s):  
Correlation Dimension ◽  
Dynamical Behavior ◽  
Recurrence Quantification Analysis ◽  
Chua Circuit ◽  
Dynamical Behaviors ◽  
Explicit Analytical Solution ◽  
Recurrence Quantification ◽  
Quantification Analysis ◽  
Dynamical Regimes ◽  
Torus Breakdown

The present study uncovers the hyperchaotic dynamical behavior of the famous Murali-Lakshmanan-Chua (MLC) circuit, when suitably modified. In the conventional MLC oscillator, an inductor is introduced in parallel between the nonlinear element and the capacitor. Many novel and interesting dynamical behaviors such as reverse period-3 doubling, torus breakdown to chaos and hyperchaos, etc., were observed. Characterization techniques includes spectrum of Lyapunov exponents, one parameter bifurcation diagram, recurrence quantification analysis, correlation dimension, etc., were employed to analyze the different dynamical regimes. Explicit analytical solution of the model is derived and the results are corroborated with the numerical outcomes.

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 PERTURBATION OF NEAR THRESHOLD EIGENVALUES: CROSSOVER FROM EXPONENTIAL TO NON-EXPONENTIAL DECAY LAWS

2011 ◽  
Vol 23 (01) ◽  
pp. 83-125 ◽  
Author(s):  
VICTOR DINU ◽  
ARNE JENSEN ◽  
GHEORGHE NENCIU
Keyword(s):  
Exponential Decay ◽  
Survival Probability ◽  
Bound States ◽  
Channel Model ◽  
Special Functions ◽  
Error Function ◽  
Small Neighborhood ◽  
Bound State ◽  
State Regime ◽  
Error Terms

For a two-channel model of the form [Formula: see text] appearing in the study of Feshbach resonances, we continue the rigorous study, begun in our paper (J. Math. Phys.50 (2009) 013516), of the decay laws for resonances produced by perturbation of unstable bound states close to a threshold. The operator H op is assumed to have the properties of a Schrödinger operator in odd dimensions, with a threshold at zero. We consider for ε small the survival probability |〈ψ0, e-itHεΨ0〉|2, where Ψ0 is the eigenfunction corresponding to E0 for ε = 0. For E0 in a small neighborhood of the origin independent of ε, the survival probability amplitude is expressed in terms of some special functions related to the error function, up to error terms vanishing as ε → 0. This allows for a detailed study of the crossover from exponential to non-exponential decay laws, and then to the bound state regime, as the position of the resonance is tuned across the threshold.

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