Construction of different wave structures, stability analysis and modulation instability of the coupled nonlinear Drinfel’d–Sokolov–Wilson model

Tariq, Kalim U.; Wazwaz, Abdul‐Majid; Javed, Rizwan

doi:10.1016/j.chaos.2022.112903

Cited by 34 publications

(8 citation statements)

References 41 publications

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“…Very recently, Modulation instabilities (MI) in a one-dimensional chain configuration of a flexible mechanical metamaterial (flexMM) is reported, here flexMMs can be modeled by a coupled system of discrete equations for the longitudinal displacements and rotations of the rigid mass units [17]. In the variety of works, many authors discussed the modulation instability analysis for metamaterials with different linear and nonlinear effects [18][19][20][21][22][23][24][25][26][27]. In these works, some novel results are attained to understand the modulation instability in metamaterials.…”

Section: Interplay Between Intermodal and Higher Order Dispersion For...mentioning

confidence: 99%

“…In [42], modulation instability influenced by nonlinear dispersion term in an optical metamaterial with the accompanying of coherent and partially coherent ultrashort pulses discussed in detail. In the realm of scientific exploration, where curiosity and innovation intertwine, a multitude of pioneering works have emerged, each unveiling the tantalizing novelty of optical soliton solutions across an array of mathematical models [43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. These mesmerizing beams of light, seemingly defying the laws of dispersion and decay, have sparked a revolution in the world of fiber optic communication systems.…”

Section: Interplay Between Intermodal and Higher Order Dispersion For...mentioning

confidence: 99%

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Interplay between intermodal and higher order dispersion for negative-index nonlinear metamaterials

Veni,

Biswas

et al. 2024

Preprint

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We have conducted a study that investigates the complex interactions between different factors in metamaterials, particularly in the context of modulation instability. We have shown the competition between intermodal dispersion, self steepening effect, higher order dispersion and the amplitude of plane waves with variety of modulation instability in metamaterials. The specific behavior of MI bands and their dependence on the self-steepening parameter and amplitude will vary depending on the details of the optical system and the dispersion properties of the medium

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Section: Interplay Between Intermodal and Higher Order Dispersion For...mentioning

confidence: 99%

Section: Interplay Between Intermodal and Higher Order Dispersion For...mentioning

confidence: 99%

Interplay between intermodal and higher order dispersion for negative-index nonlinear metamaterials

Veni,

Biswas

et al. 2024

Preprint

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“…Consequently, in the fields of engineering and the physical sciences, nonlinear differential (NLD) equations are a crucial tool for handling a wide range of natural processes. Nonlinear phenomena with a wide range of applications in solid-state physics, optical fiber, hydrodynamics, solitary wave theory, fluid dynamics, chemical kinetics, plasma, and many other domains can be explained using such models [1].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of optical solitons and sensitivity analysis in fiber optics

Raees,

Mahmood,

Hussain

et al. 2024

Preprint

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The nonlinear Schrödinger equation (NLSE) and its various forms have significant applications in the field of soliton theory. The Fokas-Lenells (FL) equation stands as a cornerstone in deepening our understanding of nonlinear wave dynamics within optical systems, particularly concerning the behavior of ultrashort pulses across different media. Its significance lies in providing a comprehensive framework to study and analyze complex phenomena, ultimately contributing to advancements in optical technology and applications. The FL equation is an integrable extension of the NLSE that provides a description of the nonlinear propagation of pulses in optical fiber. This paper seeks to discover optical soliton solutions for the FL equation by employing a modified sub-equation method. Additionally, the sensitivity analysis is described by using the various initial conditions. For the physical behavior of the models, some solutions are graphically shown in 2D, 3D and contour graphs by assigning specific values to the parameters under the provided situation at each solution. As a result, we discovered several new families of exact traveling wave solutions, such as bright solitons, dark solitons, and combined bright and dark soliton. As a result, investigated solutions have significant advantages in the field of mathematical physics. Mathematics subject classification (2020) : 39A1; 39B62; 33B10; 26A48; 26A51

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“…As a result, finding the exact solutions to the relevant NLEEs is critical for enhancing our understanding of nonlinear events and applying them to practical issues. Therefore, numerous studies have been carried out on this subject [1][2][3][4][5][6][7]. Many ways for achieving exact solutions to NLEEs have been proposed for example Lie symmetry analysis [8,9], Hirota's method [10][11][12], simplified Hirota's method [3,13], extended tanh method [14] and numerous other techniques [15,16].…”

Section: Introductionmentioning

confidence: 99%

The residual symmetry, Bäcklund transformations, CRE integrability and interaction solutions: (2+1)-dimensional Chaffee–Infante equation

Günhan Ay,

Yaşar

2023

Commun. Theor. Phys.

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In this paper, we consider the (2+1)-dimensional Chaffee–Infante equation, which occurs in the fields of fluid dynamics, high-energy physics, electronic science etc. We build Bäcklund transformations and residual symmetries in nonlocal structure using the Painlevé truncated expansion approach. We use a prolonged system to localize these symmetries and establish the associated one-parameter Lie transformation group. In this transformation group, we deliver new exact solution profiles via the combination of various simple (seed and tangent hyperbolic form) exact solution structures. In this manner, we acquire an infinite amount of exact solution forms methodically. Furthermore, we demonstrate that the model may be integrated in terms of consistent Riccati expansion. Using the Maple symbolic program, we derive the exact solution forms of solitary-wave and soliton-cnoidal interaction. Through 3D and 2D illustrations, we observe the dynamic analysis of the acquired solution forms.

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Construction of different wave structures, stability analysis and modulation instability of the coupled nonlinear Drinfel’d–Sokolov–Wilson model

Cited by 34 publications

References 41 publications

Interplay between intermodal and higher order dispersion for negative-index nonlinear metamaterials

Interplay between intermodal and higher order dispersion for negative-index nonlinear metamaterials

Dynamics of optical solitons and sensitivity analysis in fiber optics

The residual symmetry, Bäcklund transformations, CRE integrability and interaction solutions: (2+1)-dimensional Chaffee–Infante equation

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