Symbolic Computations for Nonlinear Resonances

Details Symbolic Computations for Nonlinear Resonances Symbolic Computations for Nonlinear Resonances

2007-06-26

arxiv.org/abs/0706.3789v2

Nonlinear Sciences

Pattern Formation and Solitons

39 pages, to be published as a part of the book "Extreme waves in the ocean", Springer

Scientific paper

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.

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