- Published on 15 January 2021
Nonlinear waves have long been at the research focus of both physicists and mathematicians, in diverse settings ranging from electromagnetic waves in nonlinear optics to matter waves in Bose-Einstein condensates, from Langmuir waves in plasma to internal and rogue waves in hydrodynamics. The study of physical phenomena by means of mathematical models often leads to nonlinear evolution equations known as integrable systems. One of the distinguished features of integrable systems is that they admit soliton solutions, i.e., stable, localized traveling waves which preserve their shape and velocity in the interaction. Other fundamental properties are their universal nature, and the fact that they can be effectively linearized, e.g., via the inverse scattering transform, or reduced to appropriate Riemann-Hilbert problems. Moreover, solutions can often be derived by the Zakharov-Shabat dressing method, by Backlund or Darboux transformations, or by Hirota’s method. Prototypical examples of such integrable equations in 1+1 dimensions are the nonlinear Schrödinger equation and its multicomponent generalizations, the sine-Gordon equation, the Korteweg-de Vries and the modified KdV equations, etc. In 2+1 dimensions the most notable examples are the Kadomtsev-Petviashvili (KP) equations, and the Davey-Stewartson equations. The aim of this special issue is to present the latest developments in the theory of nonlinear waves and integrable systems, and their various applications.