The soliton transform and a possible application to nonlinear Alfvén waves in space

We apply the inverse scattering transform (IST) based upon the Derivative Nonlinear Schrödinger (DNLS) equation to a complex time series of nonlinear Alfvén wave data generated by numerical simulation. The IST describes the long‐time evolution of quasi‐parallel Alfvén waves more efficiently than the Fourier transform, which is adapted to linear, not nonlinear, problems. When we add dissipation, so the conditions for the validity of the DNLS are not strictly satisfied, the IST continues to provide a compact description of the wave‐field in terms of a small number of decaying envelope solitons. Since large amplitude Alfvén waves and other nonlinear waves play essential roles in various space environments—the solar wind is one obvious example—we suggest that it may be of interest to investigate how inverse scattering transforms can be developed into practical tools for the analysis of space data.