Abstract
A (2+1)-dimensional Bossinesq–Burgers soliton equation is proposed, which has a affinitive connection with the Boussinesq–Burgers soliton hierarchy. Through a natural nonlinearization of the Boussinesq–Burgers's eigenvalue problems, a finite-dimensional Hamiltonian system is obtained and is proved to be completely integrable in Liouville sense. The Abel–Jacobi coordinates are constructed to straighten out the Hamiltonian flows, from which the quasi-periodic solutions of the (2+1)-dimensional Boussinesq–Burgers equation are derived by resorting to the Riemann theta functions.
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