On the exact soliton solutions and different wave structures to the modified Schrödinger’s equation

Abstract

Solitons are specialized solutions to certain nonlinear partial differential equations (PDEs) that behave like localized waves. They maintain their shape and speed as they propagate, interacting with other solitons through collision rather than dispersion. Our research aims to explore a wide range of fascinating and diverse soliton solutions for a modified version of Schrödinger’s equation. This modified equation has significant implications for the fields of fluid dynamics and optical fibers. To solve this model, two efficient methods are employed to reveal various forms of soliton behaviors generated by this model. We incorporate a certain combination of Jacobi elliptic functions as a key component of one of these methods to acquire exact solutions for the model. By utilizing this idea, several solutions expressed in terms of these special functions are derived which have great relevance in various areas of mathematical physics. The soliton solutions obtained in this work represent a completely novel set, distinct from those previously derived by other researchers employing alternative techniques. Furthermore, our findings will introduce new and unique configurations of soliton behaviors stemming from this model, providing insights into practical applications like fiber optic communications. Software visualization demonstrates the findings via contour plots, offering insights into potential fiber optic communication implementations. Our employed methodologies hold the potential to significantly advance the field and contribute to the development of new methodologies for tackling these challenging equations.

Keywords

• Nonlinear dispersive model
• Wave propagation
• Soliton solutions
• Schrödinger’s equation
• Integrable systems