摘要：Based on Riemann theta function and bilinear Bäcklund transformation, quasi-periodic wave solutions are constructed for an extended ( 2 + 1 ) $(2+1)$ -dimensional shallow water wave equation. A detail asymptotic analysis procedure to the one- and two-periodic wave solutions are presented, and the asymptotic properties of this type of solutions are proved. It is shown that the quasi-periodic wave solutions converge to the soliton solutions under small amplitude limits.
关键词：Riemann theta function ; soliton solutions ; quasi-periodic wave solution
