This talk is dedicated to a short review of the KP hierarchy and the 2d Toda lattice hierarchy, of their formulation in terms of Hirota equation, as well as of the geometric interpretation of the solutions as a Sato Grassmannian.
Links:
[1] https://www.mpim-bonn.mpg.de/de/taxonomy/term/39
[2] https://www.mpim-bonn.mpg.de/de/node/3444
[3] https://www.mpim-bonn.mpg.de/de/node/9419