2000/12/21 by Andrei Maimistov, Andrey I. Maimistov
Physics and Astronomy · #Advanced Fiber Laser Technologies #Breather #Burgers' equation #Dispersionless equation #Integrable system #Inverse scattering transform #Kadomtsev–Petviashvili equation #Korteweg–de Vries equation #Mathematical physics #Nonlinear Photonic Systems #Nonlinear Schrödinger equation #Nonlinear Waves and Solitons #Nonlinear optics #Nonlinear system #Physics #Quantum mechanics #Soliton #Split-step method #nlin.PS #nlin.SI #sine-Gordon equation
paper · pdf · doi:10.1007/s12043-001-0008-x
Latex, 17 pages, no figures, submitted to Pramana J
arxiv created 2000/12/21 · openalex publication_date 2001/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The models of the non-linear optics in which solitons were appeared are considered. These models are of paramount importance in studies of non-linear wave phenomena. The classical examples of phenomena of this kind are the self-focusing, self-induced transparency, and parametric interaction of three waves. At the present time there are a number of the theories based on completely integrable systems of equations, which are both generations of the original known models and new ones. The modified Korteweg-de Vries equation, the non- linear Schrodinger equation, the derivative non-linear Schrodinger equation, Sine-Gordon equation, the reduced Maxwell-Bloch equation, Hirota equation, the principal chiral field equations, and the equations of massive Thirring model are gradually putting together a list of soliton equations, which are usually to be found in non-linear optics theory.