Accurate sets of solitary solutions for the quadratic–cubic fractional nonlinear Schrödinger equation

Raghda A M Attia,A El-Sayed Ahmed,Mostafa M A Khater,M A El-Shorbagy

doi:10.1063/5.0050624

Abstract

The analytical and semi-analytical solutions to the quadratic–cubic fractional nonlinear Schrödinger equation are discussed in this research article. The model’s fractional formula is transformed into an integer-order model by using a new fractional operator. The theoretical and computational approaches can now be applied to fractional models, thanks to this transition. The application of two separate computing schemes yields a large number of novel analytical strategies. The obtained solutions secure the original and boundary conditions, which are used to create semi-analytical solutions using the Adomian decomposition process, which is often used to verify the precision of the two computational methods. All the solutions obtained are used to describe the shifts in a physical structure over time in cases where the quantum effect is present, such as wave-particle duality. The precision of all analytical results is tested by re-entering them into the initial model using Mathematica software 12.

Highlights

Many natural phenomena have been represented by nonlinear partial differential equations (NLPDEs)
Through the last five decades, these researchers, in the meantime, who succeeded in their research’s purpose, formulated powerful techniques to obtain a closed form of solutions and solitary traveling wave solutions, regarded by many as one-of-a-kind types of nonlinear partial differential equations
The exp-function properties are used for both methods to get many forms of solutions that help many researchers who do not have a background in mathematics. This similarity is not limited to these three ways, but it applies to most of the schemes in this area.33,37 ● Comparison between our solutions and that obtained in previous work: We show a comparison between our solutions and that obtained by Aslan and Inc in Ref. 38 as follows: Aslan and Inc applied the Jacobi elliptic functions to the quadratic–cubic nonlinear Schrödinger (NLS) equation when δ = 1

Summary

INTRODUCTION

Many natural phenomena have been represented by nonlinear partial differential equations (NLPDEs) Based on these models, specific studies are applied to find the approximate and exact traveling wave solutions. Specific studies are applied to find the approximate and exact traveling wave solutions These solutions help discover new characteristics of these models since the physical properties of each model play an essential role in its applications. Through the last five decades, these researchers, in the meantime, who succeeded in their research’s purpose, formulated powerful techniques to obtain a closed form of solutions and solitary traveling wave solutions, regarded by many as one-of-a-kind types of nonlinear partial differential equations..

EXPLICIT TRAVELING SOLUTIONS

Computational wave solutions via the MK method

Numerical simulation

DISCUSSION

CONCLUSION