By means of the traveling wave transformation nonlinear partial differential equations are reduced to ordinary differential equations. Applying solutions of the ordinary differential equation, we have constructed exact solutions of nonlinear partial differential equations and have obtained some exact solitary wave solutions and periodic solutions for the (2+1) dimensional Konopelchenko-Dubrovsky equation. The ordinary differential equation is directly studied and a bifurcation diagram of the system is drew. The saddle-node bifurcation which leads to jump and hysteresis is analyzed.
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温纪云,符文彬,黄琼伟,杨先林.(2+1)维KD方程的解及分岔行为[J].动力学与控制学报,2011,9(1):40~43; Wen Jiyun, Fu Wenbin, Huang Qiongwei, Yang Xianlin. Exact solution and bifurcation for (2+1) dimensional KD equation[J]. Journal of Dynamics and Control,2011,9(1):40-43.
