Nonlinear spectral analysis of ion acoustic solitary wave solutions to the forced Korteweg-de Vries equation

Solitary ion acoustic waves (solitons) in a collisionless plasma can exhibit strong stability properties even though they are nonlinear. This makes them an attractive indirect sensing mechanism for sub-cm orbital debris in low Earth orbit which is unobservable. However, observations of these solitons from spacecraft or experiment rely on visual identification because solitons are broadband in a Fourier based analysis. In this work, we numerically implement a nonlinear spectral decomposition known as the Inverse Scattering Transform and demonstrate its ability to successfully detect solitons in simulations of the Korteweg-de Vries equation, which models ion acoustic dynamics. This spectral technique is applied to simulations of solitons generated by a 10 mm spherical debris object orbiting at an altitude of 2000km interacting with the ionospheric plasma. We demonstrate the feasibility of using this technique as a real time analysis tool for screening spacecraft data for solitons.