Dynamics of novel exact soliton solutions to Stochastic Chiral Nonlinear Schrödinger Equation

Rehman, Shafqat Ur; Ahmad, Jamshad; Muhammad, Taseer

doi:10.1016/j.aej.2023.08.014

Cited by 40 publications

(3 citation statements)

References 38 publications

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“…Worth tracing to Ullah et al [ 46 ] and Salahudin et al [ 47 ] that understanding the numerical solution of the Wave Equation illuminates the propagation of waves in diverse mediums, offering indispensable tools for predicting seismic activity, designing telecommunications networks, and optimizing acoustic environments in architectural and industrial settings. As presented by Rehman et al [ 48 ] and Khan et al [ 49 ], the numerical solution of the Schrodinger Equation underpins quantum mechanical simulations, empowering scientists to unravel the intricate behaviour of fundamental particles and molecules, with applications spanning from drug discovery to the development of quantum computing algorithms. The computational exploration of the Navier-Stokes Equations was shown by Johnson [ 50 ], Fisher et al [ 51 ], and Jameson et al [ 52 ] that its solution is capable of unlocking the complexities of fluid dynamics, enabling advancements in areas crucial to human civilization, such as weather forecasting, aerodynamics, and the optimization of industrial processes, from energy production to transportation systems.…”

Section: Background Informationmentioning

confidence: 99%

Unveiling the Power of Implicit Six-Point Block Scheme: Advancing numerical approximation of two-dimensional PDEs in physical systems

Olaoluwa Omole,

Olusheye Adeyefa,

Iyabo Apanpa

et al. 2024

PLoS ONE

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In the era of computational advancements, harnessing computer algorithms for approximating solutions to differential equations has become indispensable for its unparalleled productivity. The numerical approximation of partial differential equation (PDE) models holds crucial significance in modelling physical systems, driving the necessity for robust methodologies. In this article, we introduce the Implicit Six-Point Block Scheme (ISBS), employing a collocation approach for second-order numerical approximations of ordinary differential equations (ODEs) derived from one or two-dimensional physical systems. The methodology involves transforming the governing PDEs into a fully-fledged system of algebraic ordinary differential equations by employing ISBS to replace spatial derivatives while utilizing a central difference scheme for temporal or y-derivatives. In this report, the convergence properties of ISBS, aligning with the principles of multi-step methods, are rigorously analyzed. The numerical results obtained through ISBS demonstrate excellent agreement with theoretical solutions. Additionally, we compute absolute errors across various problem instances, showcasing the robustness and efficacy of ISBS in practical applications. Furthermore, we present a comprehensive comparative analysis with existing methodologies from recent literature, highlighting the superior performance of ISBS. Our findings are substantiated through illustrative tables and figures, underscoring the transformative potential of ISBS in advancing the numerical approximation of two-dimensional PDEs in physical systems.

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Section: Background Informationmentioning

confidence: 99%

Unveiling the Power of Implicit Six-Point Block Scheme: Advancing numerical approximation of two-dimensional PDEs in physical systems

Olaoluwa Omole,

Olusheye Adeyefa,

Iyabo Apanpa

et al. 2024

PLoS ONE

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“…Nonlinear studies in oceanography, acoustics, finance, fluid mechanics and nonlinear optics have been productive [1][2][3][4][5][6][7][8]. The propagation of the picosecond pulses in an optical fiber can be described by the following nonlinear Schrödinger equation:…”

Section: Introductionmentioning

confidence: 99%

Taking into consideration a fifth-order nonlinear Schrödinger equation in an optical fiber

Wang,

Yang,

Chen

et al. 2024

Phys. Scr.

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In this paper, symbolic computation on a fifth-order nonlinear Schrödinger equation is done, for the attosecond pulses propagation in an optical fiber. With respect to the complex amplitude of the optical pulse envelope, we work out a Lax pair and derive modified generalized Darboux transformation. Then, we give the semirational solutions via the modified generalized Darboux transformation method. By means of such solutions, we graphically discuss the properties for three types of degenerate solitons.

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“…In particular, the NPSE and YTSF equation have been analyzed regarding optical fibers and engineering [37,38]. In turn, the 2D-SCNLSE [39] has been solved stochastically and the STFCB model involved in quantum optics and physics [40]. Moreover, generalized fractional calculus operators have recently received more attention and the corresponding incomplete ℵ-functions are nowadays more refined [41].…”

Section: Introductionmentioning

confidence: 99%

Fractional Fokas-Lenells equation: analyzing travelling waves via advanced analytical method

Alqudah,

Alderremy,

Mossa Al-Sawalha

et al. 2024

Phys. Scr.

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In this paper, we consider the fractional Fokas-Lenells equation, which allows us to analyze how a nonlinear optic pulse spreads in time as single-mode fiber produces higher-order nonlinear effects. We have computed perfectly accurate travelling wave solutions for the Fokas-Lenells equation using the Riccati-Bernoulli sub-Ode approach. For the corresponding equation, we have established three distinct classes of perfectly accurate travelling wave solutions with different free parameters; hyperbolic, trigonometric, and rational. A sophisticated Backlund transformation is implemented to the equation to change it to ordinary differential equation domain, leading to many extra exact solutions.

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Dynamics of novel exact soliton solutions to Stochastic Chiral Nonlinear Schrödinger Equation

Cited by 40 publications

References 38 publications

Unveiling the Power of Implicit Six-Point Block Scheme: Advancing numerical approximation of two-dimensional PDEs in physical systems

Unveiling the Power of Implicit Six-Point Block Scheme: Advancing numerical approximation of two-dimensional PDEs in physical systems

Taking into consideration a fifth-order nonlinear Schrödinger equation in an optical fiber

Fractional Fokas-Lenells equation: analyzing travelling waves via advanced analytical method

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