Relation between the Kadometsev-Petviashvili equation and the confocal involutive system

The special quasiperiodic solution of the (2 + 1)-dimensional Kadometsev-Petviashvili equation is separated into three systems of ordinary differential equations, which are the second, third, and fourth members in the well-known confocal involutive hierarchy associated with the nonlinearized Zakharov-Shabat eigenvalue problem. The explicit theta function solution of the Kadometsev-Petviashvili equation is obtained with the help of this separation technique. A generating function approach is introduced to prove the involutivity and the functional independence of the conserved integrals which are essential for the Liouville integrability. (C) 1999 American Institute of Physics. [S0022-2488(99)04207-3].