Maxwell-Bloch and nonlinear Schrodinger systems with nonzero background

This thesis is concerned with the study of two main types of nonlinear evolution equations of physical signif-icance: (i) Maxwell-Bloch (MB) systems and (ii) nonlinear Schr ̈odinger (NLS) type. Maxwell-Bloch systems characterize the nonlinear resonant interactions between coherent light and an active optical medium [10, 18]. These systems exhibit interesting optical phenomena, such as self-induced trans-parency, superfuorescence, spontaneous radiation processes, and slow light [73, 110, 120]. The nonlinear Schrodinger (NLS) equation arises as a physical model in water waves, optics, plasmas, Bose-Einstein condensates, and many other felds. In fact, it was shown that the NLS equation is a universal model for the evolution of the envelope of a weakly nonlinear dispersive wave train [23]. In some regimes, MB systems and NLS-type equations are completely integrable, with an infnitely dimensional Hamiltonian structure, and with the existence of a Lax pair. As a result, various analytical methods can be applied to study their solu-tions. In particular, a nonlinear analog of the Fourier transform—the inverse scattering transform (IST)—is a powerful technique that can solve the initial value problem (IVP) and which can be used to derive exact solutions. In general, solutions of integrable nonlinear evolution equations are comprised of solitons and radiation. Solitons are special solitary waves that retain their shapes upon propagation and interaction, while radiation is a dispersive wave.

Grantor dc:publisher

State University of New York at Buffalo

Year dc:date.issued

2018

Author dc:creator

• Li, Sitai; 0000-0002-6078-8069

Contributors dc:contributor

• Biondini, Gino
• Mathematics

• mathematics

Statement dc:rights

• Users of works found in University at Buffalo Institutional Repository (UBIR) are responsible for identifying and contacting the copyright owner for permission to reuse. University at Buffalo Libraries do not manage rights for copyright-protected works and cannot assist with permissions.
• Copyright retained by author.

Language dc:language

eng

Handle dc:identifier

http://hdl.handle.net/10477/78048

OAI record oai:identifier

https://ubir.buffalo.edu/oai/request?verb=GetRecord&metadataPrefix=qdc&identifier=oai%3Aubir.buffalo.edu%3A10477%2F78048