Optical soliton perturbation with polynomial and triple-power laws of refractive index by semi-inverse variational principle

Kohl, Russell; Biswas, Anjan; Zhou, Qin; Ekici, Mehmet; Alzahrani, Abdullah; Belić, Milivoj R.

doi:10.1016/j.chaos.2020.109765

Cited by 20 publications

(5 citation statements)

References 11 publications

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“…If one hypothetically replaces 3n with m in Eq. (49), this picture becomes very clear [2,3,5,19]. Hence, the final results of our study prove the claims declared by us.…”

Section: Discussionsupporting

confidence: 89%

“…After extensive mathematics implemented with the three integration algorithms, we have arrived at the same conclusion: the N. A. Kudryashov's model with the sextic power-law nonlinearity collapses to the special case of triple power-law format, as given by Eq. (49) [2,3,5,19]. If one hypothetically replaces 3n with m in Eq.…”

Section: Discussionmentioning

confidence: 99%

“…Kerr nonlinearity represents the most common form of self-phase modulation, when the refractive index is proportional to the intensity of light. In more general 'non-Kerr' cases, it is proportional to some function of the intensity [1][2][3][4][5]. In other words, the refractive index in the case of Kerr nonlinearity is a constant multiple of the intensity, while in a non-Kerr situation, the response of optical medium sometimes depends on the intensity raised to a positive power or, more generally, it is a sum of two terms, each of which being proportional to the intensity raised to some positive power.…”

Section: Introductionmentioning

confidence: 99%

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Optical solitons and conservation laws associated with Kudryashov�s sextic power-law nonlinearity of refractive index

Zayed¹,

Shohib²,

Alngar³

et al. 2021

Ukr. J. Phys. Opt.

160

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We recover the cases of solutions in the shape of bright, dark and singular optical solitons for the self-phase modulation effect, which belongs to the type of N. A. Kudryashov's sextic power-law nonlinearity of refractive index. Three different integration schemes have been implemented. These are a unified Riccati equation, our new mapping scheme and our addendum to the common N. A. Kudryashov's method. All of the solitons are enlisted and the criterions of their existence are mentioned. Finally, we extract three appropriate conservation laws.

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“…If one hypothetically replaces 3n with m in Eq. (49), this picture becomes very clear [2,3,5,19]. Hence, the final results of our study prove the claims declared by us.…”

Section: Discussionsupporting

confidence: 89%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optical solitons and conservation laws associated with Kudryashov�s sextic power-law nonlinearity of refractive index

Zayed¹,

Shohib²,

Alngar³

et al. 2021

Ukr. J. Phys. Opt.

160

View full text Add to dashboard Cite

show abstract

“…Many physical processes in the nonlinear sciences, including signal processing, condensed matter physics, acoustics, theoretical physics, and optical continuum creation, depend on solitonic behavior [14, 15]. The soliton solutions of several types of NLSEs have been effectively described by numerous computer analyses over the past couple of years, including the extended sinh‐Gordon equation expansion method [16], the extended Jacobi elliptic approach [17], the modified auxiliary equation mapping method [18], the modify extended direct algebraic technique [19], the inverse scattering transformation method [20], extended rational sine‐cosine method [21], the semi‐inverse variational principle [22], the generalized exponential rational function method [23, 24], the improved

\tan \left(\phi \right)

‐expansion method [25], the extended sinh‐Gordon expansion method [26], and many more [27–30].…”

Section: Introductionmentioning

confidence: 99%

“…The pairs of Equations(21,43),(22,61),(26,60), and (28,50) obtained by mapping and unified auxiliary equation methods are identical.…”

mentioning

confidence: 95%

On some soliton structures for the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity in mathematical physics

Badshah,

Tariq,

Henaish

et al. 2023

Math Methods in App Sciences

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The most important physical structure that is assumed to illustrate the geometry of optical soliton replication in optical fiber theory is the nonlinear Schrödinger equation (NLSE). Optical soliton generation in nonlinear optical fibers is a topic of great contemporary interest because of the numerous applications of ultrafast signal routing systems and short light pulses in communications. This analysis's main goal is to create a large number of soliton solutions for the dynamical model using a variety of contemporary analytical methods. This paper studies different soliton solutions to the perturbed NLSE with Kerr law nonlinearity using two sets of two distinct integration strategies: the mapping approach and the unified auxiliary equation method. The majority of solutions have been found as Jacobi elliptic functions with limiting ellipticity modulus values. Solitons like dark, bright, optical, lonely, and others are also retrieved. We were able to create various single‐type solutions with the help of these strategies. As a result, there is a variety of optical, bell‐shaped, single periodic, and multi‐periodic solutions. In order to validate the computations, the stability of the acquired findings must also be proven. The study provides a highly stunning and suitable strategy for combining numerous exciting wave demonstrations for more advanced models of the present era. Furthermore, we can assert that the outcomes reported here are unique and novel.

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Rational function solutions of higher‐order dispersive cubic‐quintic nonlinear Schrödinger dynamical model and its applications in fiber optics

Arshad,

Yasin,

Aldosary

et al. 2024

Math Methods in App Sciences

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The study explores a series of cubic‐quintic nonlinear Schrödinger equation with higher‐order dispersive characteristics. This equation is also a fundamental equation in nonlinear physics that is used to depict the dynamics of femtosecond light pulses propagating through a medium with a nonlinearity profile characterized by a parabolic function. Symbolic computation is utilized, and the double ‐expansion technique is applied to investigate the mathematical characteristics of this equation. Novel solitons and rational function solutions in various forms of the high‐order dispersive cubic‐quintic nonlinear Schrödinger equation are derived. These solutions have applications in engineering, nonlinear physics and fiber optics, providing insights into the physical nature of wave propagation in dispersive optics media. The results obtained form a basis for understanding complex physical phenomena in the described dynamical model. The computational approach employed is demonstrated to be straightforward, versatile, potent, and effective. Additionally, the presented solutions showcase various intriguing patterns, including kink‐type periodic waves, combined bright‐dark periodic waves, multipeak solitons, and breather‐type waves. This diverse set of solutions contributes to the interpretation of the dynamical model, illustrating its complexity. Moreover, the simplicity and effectiveness of our computational technique make it applicable to solving similar models in physics and other fields of applied science.

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Optical soliton perturbation with polynomial and triple-power laws of refractive index by semi-inverse variational principle

Cited by 20 publications

References 11 publications

Optical solitons and conservation laws associated with Kudryashov�s sextic power-law nonlinearity of refractive index

Optical solitons and conservation laws associated with Kudryashov�s sextic power-law nonlinearity of refractive index

On some soliton structures for the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity in mathematical physics

Rational function solutions of higher‐order dispersive cubic‐quintic nonlinear Schrödinger dynamical model and its applications in fiber optics

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