2020/07/21 by Vladimir S. Gerdjikov, Gerdjikov, Vladimir S., Michail D. Todorov +1
Mathematics · Physics and Astronomy · #35C08 #35Q51 #37K40 #Advanced Fiber Laser Technologies #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.MP #msc:35C08 #msc:35Q51 #msc:37K40 #nlin.SI
paper · pdf · doi:10.48550/arxiv.2007.10959
17 pages, 3 figures Free Boundary Problems: Theory, Experiment and Applications, July 1-4, 2020, Krasnoyarsk, Russia
arxiv created 2020/07/21 · openalex publication_date 2020/07/21 · arxiv updated 2020/07/22 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28
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.