Symbolic Computations for Nonlinear Resonances

TL;DR

This paper introduces a symbolic computation method for nonlinear resonances using a new Mathematica package, with a web interface that extends accessibility and adaptability to other software systems, demonstrated on the barotropic vorticity equation.

Contribution

Develops a symbolic computation approach for nonlinear resonances with a new Mathematica package and a web interface, adaptable to various computer algebra and numerical systems.

Findings

Symbolic computations effectively analyze nonlinear resonances.

Web interface enhances accessibility of the methods.

Application to the barotropic vorticity equation demonstrates practical utility.

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.