Abstract
A new ( 2 + 1 ) -dimensional modified BKK soliton equation is proposed, which has a close connection with the BKK soliton hierarchy. Through a natural nonlinearization of the BKK eigenvalue problems, a finite-dimensional integrable Hamiltonian system is obtained. The Abel–Jacobi coordinates are constructed to straighten out the Hamiltonian flows, from which the quasi-periodic solutions of the ( 2 + 1 ) -dimensional BKK equation are derived by resorting to the Riemann theta functions.
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