Analytical soliton solutions of the fractional order dual-mode nonlinear Schrödinger equation with time-space conformable sense by some procedures

Kopçasız, Bahadır; Yaşar, Emrullah

doi:10.1007/s11082-023-04878-7

Opt Quant Electron

2023

DOI: 10.1007/s11082-023-04878-7

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Analytical soliton solutions of the fractional order dual-mode nonlinear Schrödinger equation with time-space conformable sense by some procedures

Bahadır Kopçasız

Emrullah Yaşar

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Cited by 10 publications

References 57 publications

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Exploration of interactional phenomena and multi‐wave solutions of the fractional‐order dual‐mode nonlinear Schrödinger equation

Kopçasız,

Yaşar

2023

Math Methods in App Sciences

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This work concerns the fractional‐order dual‐mode nonlinear Schrödinger equation (FDMNLSE), which portrays the augmentation or absorption of dual waves. This model dissects the concurrent generation of two characteristic waves dealing with dual modes and introduces three physical parameters: nonlinearity, phase velocity, and dispersive factor. In the context of photonics, NLSE models the propagation of soliton pulses over intercontinental distances. Throughout this work, the fractional derivative is given in terms of time and space conformable sense. We analyze the multi‐waves method, homoclinic breather approach, and interactional solution with the double ‐functions procedure, and their applications for this equation are obtained using logarithmic transformation. The multi‐wave method is a well‐known phenomenon in nonlinear science that describes the interaction of three waves that satisfy certain resonance conditions. A breather wave is a localized and oscillatory solution that maintains its shape over time. Finally, we will discuss the dynamics of our newly obtained solutions with the help of graphs by assigning appropriate values to the parameters. The proposed methods are straight and aggressive, so the approved form can be extended for more nonlinear models. The findings are exceptional in comparison to previous findings in the literature. These outcomes may have significance for additional investigation of such frameworks to handle the nonlinear issues in applied sciences. The obtained results help us understand fluid propagation and incompressible fluids.

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Exploration of interactional phenomena and multi‐wave solutions of the fractional‐order dual‐mode nonlinear Schrödinger equation

Kopçasız,

Yaşar

2023

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

Analysis of Optical Bi-wave Solutions in a Two-mode Model Arising from the Unstable Schrödinger Equation

Al-Shara,

Alquran,

Jaradat

et al. 2024

Int J Theor Phys

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New exact solutions of the conformable space-time two-mode foam drainage equation by two effective methods

Sağlam Özkan

2024

Nonlinear Dyn

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In this article, the two-mode foam drainage equation in terms of time and space conformable sense has been investigated. Two effective methods, the generalized exponential rational function method (GERFM) and the improved version of the Bernoulli sub-equation function method (IBSEFM), are used to get new solutions of underlying equation. The fractional travelling wave transformation is applied to convert nonlinear partial differential equations to nonlinear ordinary differential equations. Proposed methods successfully extract trigonometric, hyperbolic and exponential solutions. Some of the obtained solutions are visualized to understand the effect of fractional orders of time and space derivatives on the wave profile and the dynamic behavior of the solutions.

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Analytical soliton solutions of the fractional order dual-mode nonlinear Schrödinger equation with time-space conformable sense by some procedures

Cited by 10 publications

References 57 publications

Exploration of interactional phenomena and multi‐wave solutions of the fractional‐order dual‐mode nonlinear Schrödinger equation

Exploration of interactional phenomena and multi‐wave solutions of the fractional‐order dual‐mode nonlinear Schrödinger equation

Analysis of Optical Bi-wave Solutions in a Two-mode Model Arising from the Unstable Schrödinger Equation

New exact solutions of the conformable space-time two-mode foam drainage equation by two effective methods

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