Periodic wave solutions and their limit forms of the modified Novikov equation (Q1666175)

Summary: The modified Novikov equation \(u_t - u_{t x x} +(b + 1) u^2 u_x = b u u_x u_{x x} + u^2 u_{x x x}\) is studied by using the bifurcation theory of dynamical system and the method of phase portraits analysis. The existences, dynamic properties, and limit forms of periodic wave solutions for \(b\) being a negative even are investigated. All possible exact parametric representations of the different kinds of nonlinear waves also are presented.