New generalised cubic–quintic–septic NLSE and its optical solitons

Az-Zo’bi, Emad A.; Al-Maaitah, A. F.; Tashtoush, Mohammad A.; Osman, M. S.

doi:10.1007/s12043-022-02427-7

Cited by 23 publications

(13 citation statements)

References 27 publications

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“…For example, Az-Zo'bi et al examine the generalized higher-order cubicquintic-septic NLS equation, which includes an eight-order dispersion term, employing two techniques, that is, the generalized Riccati simplest equation method (GRSEM) and the modified simple equation method (MSEM). They find a variety of optical soliton solutions, including bright, dark, and singular types, subject to certain conditions [51]. Furthermore, Az-Zo'bi et al also investigate the conformable generalized Kudryashov equation, describing pulse propagation with power nonlinearity, a higher-order equation modeling diverse wave propagation phenomena in nonlinear media.…”

Section: Applications In Nonlinear Opticsmentioning

confidence: 99%

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Modeling Wave Packet Dynamics and Exploring Applications: A Comprehensive Guide to the Nonlinear Schrödinger Equation

Karjanto

2024

Mathematics

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The nonlinear Schrödinger (NLS) equation stands as a cornerstone model for exploring the intricate behavior of weakly nonlinear, quasi-monochromatic wave packets in dispersive media. Its reach extends across diverse physical domains, from surface gravity waves to the captivating realm of Bose–Einstein condensates. This article delves into the dual facets of the NLS equation: its capacity for modeling wave packet dynamics and its remarkable breadth of applications. We illuminate the derivation of the NLS equation through both heuristic and multiple-scale approaches, underscoring how distinct interpretations of physical variables and governing equations give rise to varied wave packet dynamics and tailored values for dispersive and nonlinear coefficients. To showcase its versatility, we present an overview of the NLS equation’s compelling applications in four research frontiers: nonlinear optics, surface gravity waves, superconductivity, and Bose–Einstein condensates. This exploration reveals the NLS equation as a powerful tool for unifying and understanding a vast spectrum of physical phenomena.

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Section: Applications In Nonlinear Opticsmentioning

confidence: 99%

“…The nonlinear dispersion relationship (44) or (51) describes the relationship between the wavenumber k and the frequency ω in the dispersion plane (k, ω). Since, generally, the right-hand side of ( 44) or (51) does not vanish, any combination of (k, ω) does not always satisfy the linear dispersion relationship.…”

Section: Derivation Of the Spatial Nls Equationmentioning

confidence: 99%

Modeling Wave Packet Dynamics and Exploring Applications: A Comprehensive Guide to the Nonlinear Schrödinger Equation

Karjanto

2024

Mathematics

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“…The study of the soliton solutions explores a theoretical reference for the research of nonlinear physical models, soliton control, optical switching equipment and so on. Up to now, many effective and powerful methods have been obtained for constructing the soliton solutions of the NLPDEs, such as the soliton ansatz method [5,6], the Kudryashov method [7], the Hirota's bilinear transform method [8,9], the Darboux transformation method [10,11], the extended trial equation method [12], the Lie symmetry method [13,14], the improved F-expansion approach [15], the invariant subspace method [16,17], the extended sinh-Gordon equation expansion method [18] and the new extended auxiliary equation method [19,20], the G G ¢ ( )-expansion method [21][22][23], the Expfunction method [24,25], the modified simplest equation method [26,27], the decomposition method [28,29], and so on.…”

Section: Introductionmentioning

confidence: 99%

Chirped optical solitons and stability analysis of the nonlinear Schrödinger equation with nonlinear chromatic dispersion

Mathanaranjan

Hashemi

Rezazadeh³

et al. 2023

Commun. Theor. Phys.

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The present paper aims to investigate the chirped optical soliton solutions of nonlinear Schr¨odinger equation with nonlinear chromatic dispersion and quadratic-cubic law of refractive index. The exquisite balance between the chromatic dispersion and the nonlinearityassociated with the refractive index of a fiber gives rise to optical solitons, which can travel down the fiber for intercontinental distances. The effective technique, namely, the new extended auxiliary equation method is implemented as a solution method. Different types ofchirped soliton solutions including dark, bright, singular and periodic soliton solutions are extracted from the Jacobi elliptic function solutions when the modulus of the Jacobi elliptic function approaches to one or zero. These obtained chirped optical soliton solutions might play an important role in optical communication links and optical signal processing systems. The stability of the system is examined in the framework of modulational instability analysis.

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“…To account for this, fuzzy quantities can be used instead, resulting in what are known as fuzzy differential equations. Recently, there has been a growing interest in the analysis and applications of fuzzy differential equations, as they have found considerable use in fields such as mathematical physics [1], engineering [2], medicine [3], and others [4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method

Zureigat,

Tashtoush,

Jassar

et al. 2023

Advances in Mathematical Physics

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Complex fuzzy sets (CFSs) have recently emerged as a potent tool for expanding the scope of fuzzy sets to encompass wider ranges within the unit disk in the complex plane. This study explores complex fuzzy numbers and introduces their application for the first time in the literature to address a complex fuzzy partial differential equation that involves a complex fuzzy heat equation under Hukuhara differentiability. The researchers utilize an implicit finite difference scheme, namely the Crank–Nicolson method, to tackle complex fuzzy heat equations. The problem’s fuzziness arises from the coefficients in both amplitude and phase terms, as well as in the initial and boundary conditions, with the Convex normalized triangular fuzzy numbers extended to the unit disk in the complex plane. The researchers take advantage of the properties and benefits of CFS theory in the proposed numerical methods and subsequently provide a new proof of the stability under CFS theory. A numerical example is presented to demonstrate the proposed approach’s reliability and feasibility, with the results showing good agreement with the exact solution and relevant theoretical aspects.

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New generalised cubic–quintic–septic NLSE and its optical solitons

Cited by 23 publications

References 27 publications

Modeling Wave Packet Dynamics and Exploring Applications: A Comprehensive Guide to the Nonlinear Schrödinger Equation

Modeling Wave Packet Dynamics and Exploring Applications: A Comprehensive Guide to the Nonlinear Schrödinger Equation

Chirped optical solitons and stability analysis of the nonlinear Schrödinger equation with nonlinear chromatic dispersion

A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method

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