  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.
