Quasiperiodic solutions of the Kadomtsev–Petviashvili equation via the multidimensional Baker–Akhiezer function generated by the Broer–Kaup hierarchy

The problem of constructing quasiperiodic solutions of the Kadomtsev–Petviashvili equation is revisited. Following the idea of Krichever and the technique developed by Gesztesy and Holden, we shall explicitly construct the Baker–Akhiezer function from the compatible solutions which satisfy infinite numbers of equations in the Broer–Kaup hierarchy. Analytic and asymptotic properties will also be studied by introducing a special meromorphic function ψ1(P)ψ(P⁎)ψ1(P)ψ(P⁎), from which we derive theta function representations for the Baker–Akhiezer function and quasiperiodic solutions of the Kadomtsev–Petviashvili equation.