Cartan's structure of symmetry pseudo-group and coverings for the r-th   modified dispersionless Kadomtsev--Petviashvili equation
  We derive two non-equivalent coverings for the r-th mdKP equation from Maurer--Cartan forms of its symmetry pseudo-group. Also we find B\"acklund transformations between the covering equations. 
Oleg I. Morozov