Solving the Generalized Nonlinear Schrodinger Equation with Four-Wave Mixing: Insights into Soliton Dynamics and Interactions

Chou, Dean; Ur Rehman, Hamood; Iqbal, Ifrah; Hashemi, Mir Sajjad; Mirzazadeh, Mohammad; Bayram, Mustafa

doi:10.311581/JAMDA.2509.1014.1.2.5

Solving the Generalized Nonlinear Schrodinger Equation with Four-Wave Mixing: Insights into Soliton Dynamics and Interactions

Document Type : Research Article

Authors

Dean Chou ¹

Hamood Ur Rehman ²

Ifrah Iqbal ³

Mir Sajjad Hashemi ⁴

Mohammad Mirzazadeh ⁵

Mustafa Bayram ⁶

¹ Department of Biomedical Engineering, National Cheng Kung University, Tainan 701401, Taiwan

² Department of Mathematics, University of Okara, Okara, Pakistan

³ Department of Mathematics, University of Okara, Okara, Pakistan.

⁴ Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran.

⁵ Department of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, Rudsar-Vajargah, Iran.

⁶ Computer Engineering, Biruni University, Istanbul, Turkey.

10.311581/JAMDA.2509.1014.1.2.5

Abstract

Soliton solutions for the generalized nonlinear Schr\"{o}dinger
equation with four-wave mixing, which effectively characterize
soliton propagation in birefringent fiber, have been introduced in
this study by using three noteworthy and advanced methodologies. The
speed and direction of soliton propagation, along with the
mitigation of interactions between solitons, are influenced by the
four-wave mixing and other parameters embedded in the proposed
model. These parameters play a crucial role in governing the
dynamics of the resultant solitons. Three prominent methodologies
considered for this application include the method
$\left(\frac{1}{\chi(\zeta)},\frac{\chi'(\zeta)}{\chi(\zeta)}\right)$,
the modified extended tanh method (METM), and the new Kudryashov's method.
All three techniques have been sequentially applied to the proposed
model with successful implementation. As a result, dark, bright,
periodic singular, singular and combined dark-singular solutions are
obtained. Furthermore, an analysis of the dynamics of these
solutions is conducted through graphical representations. The
significance of our findings lies in their potential to enhance our
understanding and prediction of wave phenomena emerging in nonlinear
wave fields.

Keywords

Nonlinear Schr\" {o}dinger equation (NLSE)

Four-wave mixing

Birefringent fiber

Optical Solitons