View source for Müller-Hoissen F. A relative of the NLS equation revisited

{{MeetingTalk
| speaker = Folkert Müller-Hoissen
| title = A relative of the NLS equation revisited
| abstract = As other hierarchies, the AKNS hierarchy is known to possess a "negative" part (also see Kamchatnov and Pavlov, Phys. Lett. A 301 (2002) 269, {{arXiv|nlin/0208025}}). Via the NLS reduction, the first "negative" flow becomes a system for two functions. By elimination of one of them, the system implies a fairly simple PDE with a mixed third order derivative term. Whereas the reduction of this PDE to real dependent variable is completely integrable (i.e., a Lax pair exists), this is most likely not true for complex variable (S. Sakovich, {{arXiv|2205.09538}}). In between is the reduction given by the first negative flow of the NLS hierarchy. We present a vectorial binary Darboux transformation for the latter and exploit it to (re-) derive several types of (multi-) soliton solutions of the PDE, including rogue waves. It is derived from a general result of bidifferential calculus. Further properties of the PDE will be discussed. This work is mainly based on {{arXiv|2202.04512}}, to appear in Journal of Physics A: Mathematical and Theoretical.
| video = https://video.gdeq.org/GDEq-zoom-seminar-Pavlov60-conf-20221214-2-Folkert_Muller-Hoissen.mp4
| slides = [[Media:Mueller-Hoissen_at_Maxim_Pavlov-workshop_December_2022.pdf|Mueller-Hoissen_at_Maxim_Pavlov-workshop_December_2022.pdf]]
| references = 
| event = [[One day workshop in honor of Maxim Pavlov's 60th birthday]], 14 December 2022, Independent University of Moscow
| 79YY-MM-DD = 7977-87-85
}}