2023•Alexandria Engineering JournalOpen access

Bifurcation phase portraits and nonlinear wave solutions for the modified Konopelchenko-Dubrovsky equation

Ming Song, Shenhui Wu

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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Key concepts: Phase portrait, Bifurcation, Mathematics, Nonlinear system, Mathematical analysis, Phase (matter), Bifurcation theory, Saddle-node bifurcation