Investigation for Optical Soliton Solutions of Two Nonlinear Schrödinger Equations via Two Concrete Finite Series Methods

• Published in: International journal of applied and computational mathematics Vol. 6; no. 3
• Main Authors: Zafar, Asim, Bekir, Ahmet, Raheel, Muhammad, Rezazadeh, Hadi
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.06.2020; Springer Nature B.V
• Subjects: Applications of Mathematics; Applied mathematics; Computational mathematics; Computational Science and Engineering; Ferromagnetism; Hyperbolic functions; Mathematical analysis; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nonlinear equations; Nuclear Energy; Operations Research/Decision Theory; Original Paper; Parameters; Schrodinger equation; Series (mathematics); Solitary waves; Theoretical; Heisenberg ferromagnetic spin chains equation; Soliton solutions; Hyperbolic function method; function method; Alfvén envelop equation
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-020-00818-1

This article investigates the two cubic nonlinear Schrödinger equations which point out the evolution of disturbances in dynamics. These are ( 2 + 1 ) -dimension Heisenberg ferromagnetic spin chains equation and the ( 1 + 1 ) -dimension compressional dispersive Alfvén envelop equation. The investigation is taken in a straight forward way through two recent finite series methods namely the e x p a function and the hyperbolic function methods. The new explicit exact soliton solutions including some free parameters are obtained as fallouts of these methods. These solutions show that the proposed schemes are more simple and effective as compared to many other schemes. Additionally, the effects of the free parameters in these solutions are discussed graphically for physical interests and potential applications.