EXACT TRAVELING WAVE SOLUTIONS AND THEIR BIFURCATIONS FOR THE KUDRYASHOV–SINELSHCHIKOV EQUATION

By using the approach of dynamical systems, the bifurcations of phase portraits for the traveling system of the Kudryashov–Sinelshchikov equation with ν = δ = 0 are studied, in different parametric regions of (α, c)-parametric plane. Corresponding to different phase orbits of the traveling system, more than 26 exact explicit traveling wave solutions are derived. The dynamics of singular nonlinear traveling system is completely determined.