On the modulation instability analysis and deeper properties of the cubic nonlinear Schrödinger’s equation with repulsive δ-potential

Abstract

This projected work applies the generalized exponential rational function method to extract the complex, trigonometric, hyperbolic, dark bright soliton solutions of the cubic nonlinear Schrödinger’s equation. Moreover, trigonometric, complex, strain conditions and dark-bright soliton wave distributions are also reported. Furthermore, the modulation instability analysis is also studied in detail. To better understand the dynamic behavior of some of the obtained solutions, several numerical simulations are presented in the paper. According to the obtained results, it is clear that the method has less limitations than other methods in determining the exact solutions of the equations. Despite the simplicity and ease of use of this method, it has a very powerful performance and is able to introduce a wide range of different types of solutions to such equations. The idea used in this paper is readily applicable to solving other partial differential equations in mathematical physics.

Keywords

• The cubic nonlinear Schrödinger’s equation
• The generalized exponential rational function method
• Modulation instability analysis
• Hyperbolic and dark bright soliton solutions