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.

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Cewen Cao, Yongtang Wu, Xianguo Geng; Relation between the Kadometsev–Petviashvili equation and the confocal involutive system. J. Math. Phys. 1 August 1999; 40 (8): 3948–3970. https://doi.org/10.1063/1.532936 and may be found at https://pubs.aip.org/aip/jmp/article/40/8/3948/231488/Relation-between-the-Kadometsev-Petviashvili.