Symbolic Computations for Nonlinear Resonances
arXiv:0706.3789
Abstract
Nonlinear dynamics and pattern formation in the systems with quadratic nonlinearity is computed symbolically by specially developed MATHEMATICA package. A Web interface for the presented methods is developed, which turns the implementations from only locally available software to Web-based services that can be accessed from any computer in the Internet that is equipped with a Web browser. In particular, the results are not bound to the current Mathematica implementation but can be adapted to any other computer algebra system (e.g. Maple) or numerical software system (e.g.MATLAB) of similar expressiveness. Barotropic vorticity equation (=Hasegawa-Mima equation) with zero boundary conditions on a square is taken as a main example.
39 pages, to be published as a part of the book "Extreme waves in the ocean", Springer
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