Numerical methods for nonlinear Fourier analysis, prediction, and filtering (Q1891054)

The inverse spectral transform (ISPT) is numerically implemented to analyze arbitrary initial data for the Korteweg-de Vries equation with periodic boundary conditions and to predict the wave field at any point in spacetime without integration. The paper shows that the full ISPT (analysis and inverse analysis or prediction) is computationally inexpensive and easily applicable to a large class of problems. As an example one analyzes the organized structures generated by some partial differential equations, in which case one can quantify the nonlinear mode that gives rise to the visible structure. Another example is provided by nonlinear filtering.