The first soliton equations - sine-Gordon and KdV equation were found already in the 19th century. However the modern soliton theory with its numerous variations and applications shaped up in the 1970s. In the 1980s its deep impact on the development of Lie algebras, differential geometry,
Hamiltonian systems and many other mathematical fields became obvious.
Firstly, we will outline some of the historic moments of the solitons. Next, we will explain the main ideas of the ISM used to construct the soliton solutions of the multi-component nonlinear Schrödinger equations (MNLS). Main attention will be focused on the Riemann-Hilbert problem and Zakharov-Shabat dressing method. Finally, we will present a special class of the MNLS equations and discuss briefly their applications to Bose-Einstein condensates.
A full biography of Professor Gerdjikov can be found at https://aip.scitation.org/doi/pdf/10.1063/1.5007352
Tea/coffee will be available in room 6.314 afterwards.