Numerical solutions and analytical methods for the Kuralay equation: a path to understanding integrable systems

Alfalqi, Suleman H.; Khater, Mostafa M. A.

doi:10.1007/s11082-024-06597-z

Opt Quant Electron

2024

DOI: 10.1007/s11082-024-06597-z

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Numerical solutions and analytical methods for the Kuralay equation: a path to understanding integrable systems

Suleman H. Alfalqi,

Mostafa M. A. Khater

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2024

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Cited by 4 publications

References 25 publications

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Dynamical behavior of analytical soliton solutions to the Kuralay equations via symbolic computation

Hussain,

Ibrahim,

Birkea

et al. 2024

Nonlinear Dyn

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Dynamical behavior of analytical soliton solutions to the Kuralay equations via symbolic computation

Hussain,

Ibrahim,

Birkea

et al. 2024

Nonlinear Dyn

View full text Add to dashboard Cite

Dynamical Study with Exact Travelling Waves with High Amplitude Solitons to Clannish Random Walker’s Parabolic Equation

Majid,

Asjad,

Kumar

et al. 2024

Qual. Theory Dyn. Syst.

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On the exploration of new solitary wave solutions for the classical integrable Kuralay-IIA system of equations

Okposo,

Gómez-Agullar

et al. 2024

Phys. Scr.

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In this paper, we derive various new optical soliton solutions for the coupled Kuralay-IIA system of equations using an innovative solution approach known as the φ6−model expansion technique. This solution methodology employs a traveling wave transformation to reduce the considered problem into an easily solvable higher-order ordinary differential equation. Unlike other existing relatedmethods, this solution approach adopted here allows us to extract a rich list of diverse exact soliton solutions for the considered problem. The obtained solutions incorporate the Jacobi elliptic functions which are shown to degenerate into trigonometric and hyperbolic function solutions. These solutions exhibit distinct wave structures consisting of dark, bright, rational, periodic, singular andmixed optical solitons profiles. In exploring the impact of spatial and temporal variables on the wave patterns of the considered model, physical structures of some of the obtained solitons solutions are characterized through 3D, contour and 2D wave profiles for selected parameter values. This not only ensures the validity of the solutions as well as the constraints arising from the solution technique but also offers researchers a deeper understanding of the properties of the considered problem. The outcomes here demonstrate the applicability, versatility and efficiency of the considered solution approach for deriving diverse new soliton solutions for even more complex systems of nonlinear evolution equations.

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Numerical solutions and analytical methods for the Kuralay equation: a path to understanding integrable systems

Cited by 4 publications

References 25 publications

Dynamical behavior of analytical soliton solutions to the Kuralay equations via symbolic computation

Dynamical behavior of analytical soliton solutions to the Kuralay equations via symbolic computation

Dynamical Study with Exact Travelling Waves with High Amplitude Solitons to Clannish Random Walker’s Parabolic Equation

On the exploration of new solitary wave solutions for the classical integrable Kuralay-IIA system of equations

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