PhD Defense of Mr. Alexandre MUCCI

MUCCI Alexandre, PhLAM Laboratory - UMR8523 - Team DYSCO

Title: Bound state of solitons : localized perturbation and dissipative effect

Jury: P. SURET (PhLAM, encadrant), F. COPIE (PhLAM, encadrant), M. TLIDI (Université Libre de Bruxelles, Belgique, Rapporteur), C. FINOT (Université de Bourgogne, Rapporteur), A. KUDLINSKI (PhLAM, membre), B. BARVIAU (Université de Rouen, membre)

Abstract:

In nonlinear physics, a special wave called the fundamental soliton has attracted significant attention due to its critical role in dynamic systems. Its unique properties include maintaining both temporal and spectral shape during propagation, as well as demonstrating resilience when interacting with other nonlinear waves. This thesis investigates these nonlinear waves in the context of light propagation in single-mode optical fibers, which at leading order are governed by the one-dimensional nonlinear Schrödinger equation (1D-NLSE), an integrable system solvable via the inverse scattering transform (IST) method. The primary objective of this work is to experimentally validate results derived from a novel IST perturbation theory, specifically developed for a unique solution within the 1D-NLSE: bound states of solitons, which enable the manipulation of soliton velocities within this solution. Additionally, the thesis explores the interaction of soliton eigenvalues in the IST spectrum—representing solitons present in the initial potential—under the influence of higher-order perturbative effects such as dissipation.