Bifurcation analysis for mixed derivative nonlinear Schrödinger’s equation , $$\alpha $$-helix nonlinear Schrödinger’s equation and Zoomeron model

Rizvi, Syed T. R.; Seadawy, Aly R.; Naqvi, S. Kamran; Ismail, Muhammad

doi:10.1007/s11082-023-06100-0

Opt Quant Electron

2024

DOI: 10.1007/s11082-023-06100-0

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Bifurcation analysis for mixed derivative nonlinear Schrödinger’s equation , $$\alpha $$-helix nonlinear Schrödinger’s equation and Zoomeron model

Syed T. R. Rizvi,

Aly R. Seadawy,

S. Kamran Naqvi

et al.

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2024

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Cited by 3 publications

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Variational principle for generalized unstable and modify unstable nonlinear Schrödinger dynamical equations and their optical soliton solutions

Seadawy,

Alsaedi

2024

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Variational principle for generalized unstable and modify unstable nonlinear Schrödinger dynamical equations and their optical soliton solutions

Seadawy,

Alsaedi

2024

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New exact optical soliton solutions of the derivative nonlinear Schrödinger equation family

Aydemir

2024

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In this study, we use a systematic approach named the generalized unified method (GUM) to construct the general exact solutions of the derivative nonlinear Schrödinger (DNLS) family that also includes perturbed terms, which are the Kaup–Newell equation, the Chen–Lee–Liu equation, and the Gerdjikov–Ivanov equation. The GUM provides more general exact solutions with free parameters for nonlinear partial differential equations such that some solutions obtained by different exact solution methods, including the hyperbolic function solutions, the trigonometric function solutions, and the exponential solutions, are derived from these solutions by giving special values to these free parameters. Additionally, the used method reduces a large number of calculations compared to other exact solution methods, enabling computations to be made in a short, effortless, and elegant way. We investigate the DNLS family in this work because of its extensive applications in nonlinear optics. Particularly, the obtained optical soliton solutions of the DNLS family are useful for describing waves in optics and facilitating the interpretation of the propagation of solitons through optical fibers. Furthermore, this work not only contributes significantly to the advancement of soliton dynamics and their applications in photonic systems but also be productively used for more equations that occur in mathematical physics and engineering problems. Finally, 2D and 3D graphs of some derived solutions are plotted to illustrate behaviors of optical soliton.

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Investigating the generalized Kudryashov’s equation in magneto-optic waveguide through the use of a couple integration techniques

Zayed,

Al-Nowehy,

Arnous

et al. 2024

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Bifurcation analysis for mixed derivative nonlinear Schrödinger’s equation , $$\alpha $$-helix nonlinear Schrödinger’s equation and Zoomeron model

Cited by 3 publications

References 43 publications

Variational principle for generalized unstable and modify unstable nonlinear Schrödinger dynamical equations and their optical soliton solutions

Variational principle for generalized unstable and modify unstable nonlinear Schrödinger dynamical equations and their optical soliton solutions

New exact optical soliton solutions of the derivative nonlinear Schrödinger equation family

Investigating the generalized Kudryashov’s equation in magneto-optic waveguide through the use of a couple integration techniques

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