Cubic-quartic optical solitons with Kudryashov’s law of refractive index by Lie symmetry analysis

Kumar, Sachin; Malik, Sandeep

doi:10.1016/j.ijleo.2021.167308

Cited by 22 publications

(6 citation statements)

References 35 publications

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“…Figure 2 illustrates the evolution of soliton solution (21), where the wave profile shows an M-shaped (two-hump) soliton. The graph in Figure 3 demonstrates periodic singular wave of solution (23). Moreover, Figure 4 presents the plot of solution (25) that describes the bright soliton wave.…”

Section: Resultsmentioning

confidence: 98%

“…However, the complex-valued amplitude for some of these solutions can be converted into real value. For example, the periodic solution (23) has the form…”

Section: Elucidation Of Schemementioning

confidence: 99%

“…One of the most popular technologies employed in the research studies is based on adding another form of dispersion such as Bragg gratings dispersion, pure-cubic dispersion, pure-quartic dispersion, cubic-quartic dispersion and many others. For example, the combination of fourth-order dispersion (4OD) and third-order dispersion (3OD) terms can completely compensate for low CD and gives rise to creation of the so-called cubic-quartic (CQ) solitons, see the references [19][20][21][22][23][24]. Later, the model of FLE is developed to include 4OD and 3OD terms and that means CQ solitons can be constructed in polarization preserving fibers [25][26][27].…”

Section: Introductionmentioning

confidence: 99%

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Cubic–quartic optical soliton perturbation and modulation instability analysis in polarization-controlled fibers for Fokas–Lenells equation

Al-Ghafri¹,

Krishnan²,

Biswas³

2022

J. Eur. Opt. Society-Rapid Publ.

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The objective of this study is to investigate miscellaneous wave structures for perturbed Fokas–Lenells equation (FLE) with cubic-quartic dispersion in polarization-preserving fibers. Based on the improved projective Riccati equations method, various types of soliton solutions such as bright soliton, combo dark–bright soliton, singular soliton and combo singular soliton are constructed. Additionally, a set of periodic singular waves are also retrieved. The dynamical behaviors of some obtained solutions are depicted to provide a key to understanding the physics of the model. The modulation instability of the FLE is reported by employing the linear stability analysis which shows that all solutions are stable.

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Section: Resultsmentioning

confidence: 98%

“…However, the complex-valued amplitude for some of these solutions can be converted into real value. For example, the periodic solution (23) has the form…”

Section: Elucidation Of Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Cubic–quartic optical soliton perturbation and modulation instability analysis in polarization-controlled fibers for Fokas–Lenells equation

Al-Ghafri¹,

Krishnan²,

Biswas³

2022

J. Eur. Opt. Society-Rapid Publ.

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“…Scientific areas such as fluid dynamics, chemistry, plasma physics, mathematical biology, solid-state physics, optical fibers and plasma physics all seek precise nonlinear partial differential equations (PDEs). Inverse scattering transform method [1], Darboux transformation [2,3], Lie symmetry method [4], Bäcklund transformation [5], variable separation approach [6], Truncated Painlevé Approach and Hirota bilinear method [7] are just a few of the approaches that researchers are carrying out continuously on developing to resolve nonlinear evolution equations. It is possible to build localized coherent structures from the solution, including solitons [8,9], dromions [10], rogue waves [11], lumps [12] and breathers [13].…”

Section: Introductionmentioning

confidence: 99%

Non-collisional Behaviour of Novel Nonlinear Wave Patterns for (2+1) Dimensional Fokas System

Thilakavathy

Amrutha²,

Sivatharani

et al. 2023

Preprint

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This paper investigates the most straightforward extension of the (2+1) dimensional NLS equation, termed the Fokas system. The evolution equation is trilinearized, employing a unique method called Truncated Painlev\'{e} Approach for the (2+1) dimensional Fokas system. In terms of arbitrary functions, this method finds relatively extensive classes of solutions. Localized solutions, including dromion triplet, lump, multi-compacton and multi-rogue wave are generated by efficiently utilizing arbitrary functions. The analysis reveals that the localized solutions evolved do not move in space and only their amplitude changes with time.

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“…There are many methods to construct the exact solutions of FPDEs such as similarity reduction method [17][18][19][20][21][22][23][24][25], ¢ G G method [26][27][28], tanh method [29,30], Extended sinh-Gordon equation expansion method (EShGeem) [31], Jacobi elliptic function method [32,33] and Kudryashov method [34,35] etc. The Lie symmetry reduction method is an efficient method to obtain the exact solutions of NLPDEs.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis, chaotic analysis and diverse optical soliton solutions of time-fractional (2+1) dimensional generalized Camassa-Holm Kadomtsev-Petviashvili equation arising in shallow water waves

Gupta

2023

Phys. Scr.

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This paper presents a study on (2+1) generalized Camassa-Holm Kadomtsev-Petviashvili equation, which is used to describe the behavior of shallow water waves in nonlinear media. The considered equation provides a more accurate description of wave behavior compared to linear wave equations and can account for wave breaking and other nonlinear effects. This model can be used to describe and study the behavior of nonlinear waves such as rogue waves in complex fluid dynamics scenarios. This includes the behavior of waves in stratified fluids, nonlinear dispersive media and wave interactions in fluid flows with varying velocities and densities. Bifurcation analysis of the governing equation has been performed using the planar dynamical system method. The chaotic behavior of the dynamical system has been examined by utilizing various techniques such as time series analysis and construction of 2D and 3D phase space trajectories. Furthermore, introduction of perturbed term has resulted in the observation of chaotic and quasi-periodic behaviors across a range of parameter values. The considered equation has been reduced to ordinary differential equation by performing symmetry reduction. Kudryashov method has been used to obtain exact solution of reduced equation. Single soliton solution of governed equation has been obtained by using Hirota method and impact of fractional parameter on the obtained solution has been studied using graphical representation. The extended sinh-Gordon equation expansion method and modified generalized exponential rational function method have been exploited to obtain dark, bright and singular soliton of considered equation. The motivation for this study arises from need to understand and analyze the complex dynamics of shallow water waves in nonlinear media with a particular focus on governing equation. By performing symmetry reduction and applying various analytical methods, we aim to unravel the intricate behavior and soliton solutions of considered equation, contributing to broader understanding of nonlinear wave phenomena. 

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Cubic-quartic optical solitons with Kudryashov’s law of refractive index by Lie symmetry analysis

Cited by 22 publications

References 35 publications

Cubic–quartic optical soliton perturbation and modulation instability analysis in polarization-controlled fibers for Fokas–Lenells equation

Cubic–quartic optical soliton perturbation and modulation instability analysis in polarization-controlled fibers for Fokas–Lenells equation

Non-collisional Behaviour of Novel Nonlinear Wave Patterns for (2+1) Dimensional Fokas System

Bifurcation analysis, chaotic analysis and diverse optical soliton solutions of time-fractional (2+1) dimensional generalized Camassa-Holm Kadomtsev-Petviashvili equation arising in shallow water waves

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