Phase portraits and optical soliton solutions of coupled nonlinear Maccari systems describing the motion of solitary waves in fluid flow
Zhao Li, Xinyu Xie, Changjiang Jin
Abstract
The coupled nonlinear Maccari systems are very important equations which have been developed vigorously in the fields of the nonlinear optics, deep water theory, plasma physics, nonlinear optics and so on. The main work of this paper is focus on the bifurcation analysis and single optical soliton solutions of the coupled nonlinear Maccari systems describing the motion of solitary waves in the nonlinear optics. Firstly, the coupled nonlinear Maccari systems are reduced to the nonlinear ordinary differential equations by employing traveling wave transformation and linear transformation. Secondly, the phase portraits of coupled nonlinear Maccari systems are drawn. Moreover, the optical soliton solutions of the coupled nonlinear Maccari systems are obtained by using the planar dynamic system method and the polynomial complete discriminant system method, respectively. The Jacobian function solutions, the hyperbolic function solutions, the trigonometric function solutions and the rational function solutions are constructed. Finally, three-dimensional diagram and two-dimensional diagram of the coupled nonlinear Maccari systems are drawn.