Introduction to the Nonlinear Resonance Analysis (NRA)
Sprache des Vortragstitels:
The NRA is a part of mathematical physics dealing with nonlinear wave resonances observed in real physical systems. From pure mathematical point of view , the NRA can be regarded as a generalization of the classical Fourier analysis to the case of a nonlinear partial differential equations (PDE) with dispersive linear part and with nonlinear part being small in some well-defined sense. Resonance conditions have the form of a Diophantine equation.
In this talk I introduce the main ideas of the NRA and formulate its important theoretical results. Examples of application of the NRA for interpreting the results of a laboratory experiment (with water waves) and for describing natural phenomenon (the Earth's atmosphere) will be briefly presented