Abstract
The Kadomtsev-Petviashvili (KP) equation is separated into systems of compatible ordinary differential equations with the help of two (1+1)-dimensional soliton equations. Quasi-periodic solution of the KP equation is finally obtained in terms of Riemann theta functions. During that course, the generating function approach is used to prove the involutivity and the functional independence of the conserved integrals, and the Abel-Jacobi coordinates are introduced to linearize the associated flows.
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