Qualitative analysis and modulation instability for the extended (3+1)-dimensional nonlinear Schrödinger equation with conformable derivative

Abstract

The focus of the article studies the qualitative analysis and modulation instability for the extended (3+1)-dimensional nonlinear Schrödinger equation with conformable derivative. Firstly, the extended (3+1)-dimensional nonlinear Schrödinger equation with conformable derivative is transformed into two-dimensional planar dynamic system through complex exponential wave transformation. Secondly, phase portrait and its orbit of the system are analyzed through the theory of dynamical system. By using Maple software the phase portrait, Poincaré section and sensitivity analysis are compared and displayed. Finally, parameter conditions for stable systems are provided through modulation instability.

Keywords

• Conformable derivative
• Planar dynamic system
• Sensitivity analysis
• Modulation instability