Studies of Nonlinear Physics

Dear Colleagues,

At variance with textbook examples, nonlinear effects play a crucial role in every physical system: interactions between different parts and states of a system depend inherently by how much these parts or states are populated. Let us consider wave propagation phenomena modelled by a nonlinear partial differential equation (PDE). Examples include propagation of intense laser pulses, evolution of a Bose-Einstein condensate, surface and internal waves in hydrodynamics, Langmuir waves in plasmas. Since the 1970s, several PDEs were discovered to exhibit the important mathematical property of integrability (i.e., they generalise the concept of Liouville integrability to infinite-dimensional systems and are solvable by means of the inverse scattering transform). They possess some special families of exact solutions, such as solitons, breathers, kinks, etc. Moreover, these models (Korteweg–de Vries, Nonlinear Schrödinger, Kadomtsev–Petviashvili equations, etc.) proved to be universal: many physical phenomenona can be approximately described by them in some specific range of parameters. Conservative and non-conservative (forced-damped) extensions of each of them provide a powerful toolbox for physicists.

In this Special Issue, we invite submissions exploring the above-mentioned nearly integrable extensions of integrable models. Contributions can focus on (just to mention a few) frequency combs in optics, nonlinear optics in micro- and nanostructures, wind-forced oceanic waves in the gravity and capillary regimes, population dynamics in biology and human society, finance, etc. Survey papers and reviews are also welcomed.

Dr. Andrea Armaroli
Guest Editor

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