On Asymptotic Dynamical Regimes of Manakov $N$-soliton Trains in Adiabatic Approximation
| Autor: | Vladimir S. Gerdjikov, Michail D. Todorov |
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| Rok vydání: | 2020 |
| Předmět: |
Physics
Nonlinear Sciences - Exactly Solvable and Integrable Systems Integrable system General Mathematics General Physics and Astronomy FOS: Physical sciences Mathematical Physics (math-ph) Adiabatic theorem Matrix (mathematics) Nonlinear Sciences::Exactly Solvable and Integrable Systems Chain (algebraic topology) Bound state Manakov system Soliton Statistical physics Exactly Solvable and Integrable Systems (nlin.SI) Nonlinear Sciences::Pattern Formation and Solitons Mathematical Physics Eigenvalues and eigenvectors 35C08 35Q51 37K40 |
| DOI: | 10.48550/arxiv.2007.10959 |
| Popis: | We analyze the dynamical behavior of the $N$-soliton train in the adiabatic approximation of the Manakov model. %perturbed by gain/loss effects and also by several types of external potentials. 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. Comment: 17 pages, 3 figures Free Boundary Problems: Theory, Experiment and Applications, July 1-4, 2020, Krasnoyarsk, Russia |
| Databáze: | OpenAIRE |
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