Some optical soliton solutions with bifurcation analysis of the paraxial nonlinear Schrödinger equation

Islam, S. M. Rayhanul; Arafat, S. M. Yaisir; Alotaibi, Hammad; Inc, Mustafa

doi:10.1007/s11082-023-05783-9

Opt Quant Electron

2024

DOI: 10.1007/s11082-023-05783-9

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Some optical soliton solutions with bifurcation analysis of the paraxial nonlinear Schrödinger equation

S. M. Rayhanul Islam,

S. M. Yaisir Arafat,

Hammad Alotaibi

et al.

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Cited by 11 publications

References 32 publications

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Exploring the fractional effect to the optical wave propagation for the extended Kairat-II equation

Muhammad,

Rehman,

Nasreen

et al. 2024

Nonlinear Dyn

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Exploring the fractional effect to the optical wave propagation for the extended Kairat-II equation

Muhammad,

Rehman,

Nasreen

et al. 2024

Nonlinear Dyn

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On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

Ozisik,

Esen,

Secer

et al. 2024

Opt Quant Electron

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In this work, we take into account the (2+1)-Davey Stewartson equation (DSE) and the (2+1)-complex coupled Maccari system (CCMS) and their analytical solutions. Besides, we tackle the role of the problem parameters on the soliton behavior produced by the presented DSE. Exact traveling wave solutions are highly useful in numerical and analytical theories for such equations. While numerical methods are widely used, improving analytical approaches for obtaining analytical solutions is necessary for a deeper understanding of dynamics. This study marks a significant milestone by implementing the efficient analytical approach, enhanced modified extended tanh expansion method, for the first time to the (2+1)-DSE and (2+1)-CCMS equations, thereby making a notable contribution to the existing literature. We have shown that features of the soliton solutions can represent the spread of propagation on the wavefronts and show a reasonable dependency on parameter values. Some of the solutions discovered in three- and two-dimensional arrangements can also be described in graphic representations of their behavior. With the help of the graphical depictions, bright, singular, and periodic singular soliton characters for the $$(2+1)$$ ( 2 + 1 ) -DSE and singular, dark, bright, and periodic singular soliton characters for the $$(2+1)$$ ( 2 + 1 ) -CCMS are acquired. The results show that the utilized analytical technique is easily applicable, efficient, reliable, robust, and categorical when it comes to finding analytical solutions for different nonlinear models. Moreover, the problem parameters and the coupling coefficients have significant influences on the behavior of the solitons of the DSE, and this examination is studied for the first time in this article.

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Exploring exact solitary wave solutions of Kuralay-II equation based on the truncated M-fractional derivative using the Jacobi Elliptic function expansion method

Farooq,

Ma,

Khan

2024

Opt Quant Electron

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Some optical soliton solutions with bifurcation analysis of the paraxial nonlinear Schrödinger equation

Cited by 11 publications

References 32 publications

Exploring the fractional effect to the optical wave propagation for the extended Kairat-II equation

Exploring the fractional effect to the optical wave propagation for the extended Kairat-II equation

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

Exploring exact solitary wave solutions of Kuralay-II equation based on the truncated M-fractional derivative using the Jacobi Elliptic function expansion method

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