Optical Solitons and Conservation Laws for the Concatenation Model: Undetermined Coefficients and Multipliers Approach

Biswas, Anjan; Vega-Guzmán, José; Kara, A. H.; Khan, Salam; Triki, Houria; González-Gaxiola, O.; Moraru, Luminița; Georgescu, Puiu Lucian

doi:10.3390/universe9010015

Cited by 37 publications

(11 citation statements)

References 25 publications

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“…The surface plots are also included so that an illustrative effect is also displayed beside the analytically located solutions. It needs to be noted that the dark and singular solitons that are derived in this work are comparable to the ones that have been reported earlier [3][4][5]. While no other analytical methods are applicable since an exhaustive set of solutions are recovered, at least as far as single soliton solutions are concerned.…”

Section: Discussionsupporting

confidence: 78%

“…The dynamics of optical solitons has been sustained for half a century since its first inception in 1973. There are enumerable advances to soliton science, especially in the field of optoelectronics and telecommunications engineering [1][2][3][4][5][6][7][8][9][10]. There are several forms of solitons that have been addressed in this context in the field of quantum optics.…”

Section: Introductionmentioning

confidence: 99%

“…A first attempt was proposed during 2014 as a concatenation of the pre-existing nonlinear Schrodinger's equation (NLSE), Lakshmanan-Porsezian-Daniel (LPD) model and the Sasa-Satsuma (SS) equation [1,2]. This gave way to the newly proposed concatenation model [1][2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

“…This concatenation model has been studied earlier, where many of its other features have been addressed. These include Painleve analysis [5], conservation laws [4], undetermined coefficients [4], reduction to ordinary differential equations by traveling wave hypothesis [3] and other such analytical methodologies. The numerical issues have also been addressed where bright and dark solitons have been recovered numerically by the application of the Laplace-Adomian decomposition scheme [10].…”

Section: Introductionmentioning

confidence: 99%

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Optical Solitons for a Concatenation Model by Trial Equation Approach

et al. 2022

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This paper addresses the newly proposed concatenation model by the usage of trial equation approach. The concatenation is a chain model that is a combination of the nonlinear Schrodinger’s equation, Lakshmanan–Porsezian–Daniel model as well as the Sasa–Satsuma equation. The recovered solutions are displayed in terms of dark solitons, singular solitons, cnoidal waves and singular periodic waves. The trial equation approach enables to recover a wide spectrum of solutions to the governing model. The numerical schemes give a visual perspective to the solutions derived analytically.

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Section: Discussionsupporting

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optical Solitons for a Concatenation Model by Trial Equation Approach

et al. 2022

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“…In mathematical physics, it is very important to find exact solutions to nonlinear differential equations [1,2,3,4,5]. Exact solutions play a crucial role in understanding various qualitative and quantitative features of nonlinear phenomena [6].…”

Section: Introductionmentioning

confidence: 99%

A simplified symbolic computation method based on Hirota bilinear equations for constructing multiple-order rogue waves

Tang,

Zeng

2024

Preprint

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The computation of higher-order rogue waves can be a time-consuming process.Hirota bilinear equations with controllable centers for all orders of rogue wave solutions can be solved by a simplified symbolic computation method.Only one-third of the computational effort needed by the original method is required by the simplified one, for very high orders. For instance, simpler first- to fourth-order rogue waves, as well as fifth-order rogue waves that were previously unpublished, are yielded by the simplified method for a generalized (2+1)-dimensional Kadomtsev-Petviashvili equation. To be honest, the obtained results in this paper substantially improve or complement the corresponding conditions in the references [17,18]. As a consequence,~this paper gives a new idea to derive high-order rogue waves for the generalized (2+1)-dimensional Kadomtsev-Petviashvili equation.

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Dynamics of optical solitons in the extended (3+1)‐dimensional nonlinear conformable Kudryashov equation with generalized anti‐cubic nonlinearity

Mirzazadeh,

Hashemi,

Akbulu

et al. 2024

Math Methods in App Sciences

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The nonlinear Schrödinger equation (NLSE) is a fundamental equation in the field of nonlinear optics and plays an important role in the study of many physical phenomena. The present study introduces a new model that demonstrates the novelty of the paper and provides the advancement of knowledge in the area of nonlinear optics by solving a challenging problem known as the extended ‐dimensional nonlinear conformable Kudryashov's equation (CKE) with generalized anti‐cubic nonlinearity, which is a generalization of the NLSE to three spatial dimension and one temporal dimension for the first time. This work is significant because it advances our understanding of nonlinear optics and its applications to solve complex equations in physics and related disciplines. The extended hyperbolic function method (EHFM) and Nucci's reduction method are applied to the extended ‐dimensional nonlinear CKE with generalized anti‐cubic nonlinearity. The equation is solved by using the concept of conformable derivative, a recently developed operator in fractional calculus, which has advantages over other fractional derivatives in terms of accuracy and flexibility. The attained solutions include periodic singular, dark 1‐soliton, singular 1‐soliton, and bright 1‐soliton which are visualized using 3D and contour plots. This study highlights the potential of using conformable derivative and the applied techniques to solve complex nonlinear differential equations in various fields. The obtained solutions and analysis will be useful in the design and analysis of optical communication systems and other related fields. Overall, this study contributes for the understanding of the dynamics of the extended ‐dimensional nonlinear CKE and offers new insights into the use of mathematical techniques to tackle complex problems in physics and related fields.

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Optical Solitons and Conservation Laws for the Concatenation Model: Undetermined Coefficients and Multipliers Approach

Cited by 37 publications

References 25 publications

Optical Solitons for a Concatenation Model by Trial Equation Approach

Optical Solitons for a Concatenation Model by Trial Equation Approach

A simplified symbolic computation method based on Hirota bilinear equations for constructing multiple-order rogue waves

Dynamics of optical solitons in the extended (3+1)‐dimensional nonlinear conformable Kudryashov equation with generalized anti‐cubic nonlinearity

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