Abstract
The bifurcation phase portraits and exact nonlinear wave solutions of the modified Konopelchenko-Dubrovsky (KD) equation are studied by using the bifurcation method. The bifurcation phase portraits of the modified KD equation are given when a>0 and a<0. When different combinations of the parameters a, b, k and n, eighteen new exact nonlinear wave solutions for the modified KD equation are obtained.
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