Investigation of travelling wave solutions for the (3 + 1)-dimensional hyperbolic nonlinear Schrödinger equation using Riccati equation and F-expansion techniques

• Published in: Optical and quantum electronics Vol. 55; no. 11
• Main Authors: Ali, Mohamed R., Khattab, Mahmoud A., Mabrouk, S. M.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.11.2023; Springer Nature B.V
• Subjects: Characterization and Evaluation of Materials; Computer Communication Networks; Electrical Engineering; Electromagnetic fields; Exact solutions; Graphical representations; Lasers; Optical Devices; Optics; Photonics; Physics; Physics and Astronomy; Riccati equation; Schrodinger equation; Solitary waves; Traveling waves; Water waves; F-expansion principle; Riccati equation method; Travelling wave solutions; Solitons; Hyperbolic non-linear Schrödinger equations
• ISSN: 0306-8919; 1572-817X
• DOI: 10.1007/s11082-023-05236-3

The (3 + 1)-dimensional hyperbolic nonlinear Schrödinger equation (HNLS) is used as a model for different physical phenomena such as the propagation of electromagnetic fields, the dynamics of optical soliton promulgation, and the evolution of the water wave surface. In this paper, new and different exact solutions for the (3 + 1)-dimensional HNLS equation is emerged by using two powerful methods named the Riccati equation method and the F-expansion principle. The behaviors of resulting solutions are different and expressed by dark, bright, singular, and periodic solutions. The physical explanations for the obtained solutions are examined by a graphical representation in 3d profile plots.