A multidimensional superposition principle: numerical simulation and analysis of soliton invariant manifolds. I

The author presents a numerical technique for the analysis of soliton invariant manifolds in the framework of a multidimensional superposition principle for nonlinear PDEs. The ideas and implementation details are illustrated via various examples: the KdV equation, the MKdV equation, the Kawahara equation, the regularized long wave equation and soliton models.