A family of nonlinear Schrodinger equations and their solitons solutions

El-Nabulsi, Rami Ahmad; Anukool, Waranont

doi:10.1016/j.chaos.2022.112907

Cited by 28 publications

(6 citation statements)

References 105 publications

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“…We can write the equations of motion (36) in terms of Laplacian potentials X a (λ) and A a (λ) associated to the functions x α,a (λ) and A α,a (λ) and defined by Equation (12). The result takes the following form…”

Section: Equations Of Motionmentioning

confidence: 99%

“…Conversely, the Laplacian potentials corresponding to the particle's coordinates in a constant electric field, as revealed by Equations ( 55) and (56), are solutions to ordinary differential equations that do not explicitly exhibit dependence on α. According to the definition provided in Equation (12), the exchange between fractional and ordinary differ-ential equations occurs at the expense of encapsulating all information about fractionality within the definition of the Laplacian potentials. Consequently, Equations ( 55) and (56) bear a resemblance to the classical particle's trajectory.…”

Section: Flsp In Constant Electric Fieldmentioning

confidence: 99%

“…The fractional Laplacian is a non-local pseudo-differential operator that has recently been used to model and investigate a wide range of physical and mathematical physical systems [1]. Models based on the fractional Laplacian have been successfully used to analyze the absorption and dispersion of compressional and shear waves in viscoelastic solids [2], fractional diffusion theory [3], non-linear fractional MOND-like gravity [4] and the Kuzmin-like gravitational model [5], the Scott correction for few electrons in atoms [6,7], the non-locality of the Pippard kernel in superconductivity and anomalous dimension for holographic conserved currents [8], long-distance processes that characterize tracer transport in both subsurface and surface environments [9], Polyakov's confinement mechanism for Maxwell's equations [10], soliton stabilization in d = 1 with possible applications to Bose-Einstein condensates [11], solitonic solutions to the non-linear Schroedinger equation [12], the quantization of non-local scalar fields with an extension problem [13], the conformal invariance in the long-range Ising model [14] and non-local scalar fields with an extension problem [15], just to mention a few applications across the spectrum of physics.…”

Section: Introductionmentioning

confidence: 99%

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Fractional Laplacian Spinning Particle in External Electromagnetic Field

Porto,

Godinho,

Vancea

2023

Dynamics

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We construct a fractional Laplacian spinning particle model in an external electromagnetic field that generalizes a standard relativistic spinning particle model without anti-commuting spin variables. The one-dimensional fractional Laplacian in world-line variable λ governs the kinetic energy that is non-local in λ. The interaction between the particle’s charge and the electromagnetic four-potential is non-local in λ, while the interaction between the particle’s spin tensor and the electromagnetic field is standard. By applying the variational principle, we obtain the equations of motion for particle coordinates. We solve analytically the equations of motion in two particular cases: the constant electric and magnetic field. For more complex field configurations, the equations are, in general, non-local and non-linear. By making the assumption of a much weaker interaction term between the charge and four-potential compared with the interaction between spinning degrees of freedom and the electromagnetic field, we obtain approximate analytical solutions in the case of a quadratic electromagnetic potential.

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Section: Equations Of Motionmentioning

confidence: 99%

Section: Flsp In Constant Electric Fieldmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fractional Laplacian Spinning Particle in External Electromagnetic Field

Porto,

Godinho,

Vancea

2023

Dynamics

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“…Many scholars have explored various nonlinear frameworks in previous studies to comprehend the dynamics of solitons. Noteworthy among these models are the Schrödinger equation [18], Yu-Toda-Sasa-Fukuyama (YTSF) model [19], Fokas-Lenells model [20], Oskolkov model [21], Kadomtsev-Petviashvili (KP) model [22], and Sakovich equation [23].…”

Section: Introductionmentioning

confidence: 99%

Unveiling multi-wave patterns: dynamic characterization and sensitivity analysis of the Yu-Toda-Sasa-Fukuyama model in lattice and liquid

Riaz,

Kazmi,

Jhangeer

2024

Phys. Scr.

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In this study, an examination of the Yu-Toda-Sasa-Fukuyama equation is undertaken, a model that characterizes elastic waves in a lattice or interfacial waves in a two layer liquid. Our emphasis lies in conducting a comprehensive analysis of this equation through various viewpoints, including the examination of soliton dynamics, exploration of bifurcation patterns, investigation of chaotic phenomena, and a thorough evaluation of the model's sensitivity. Utilizing a simplified version of Hirota's approach, multi-soliton pattens, including 1-wave, 2-wave, and 3-wave solitons, are successfully derived. The identified solutions are depicted visually via 3D, 2D, and contour plots using Mathematica software. The dynamic behavior of the discussed equation is explored through the theory of bifurcation and chaos, with phase diagrams of bifurcation observed at the fixed points of a planar system. Introducing a perturbed force to the dynamical system, periodic, quasi-periodic and chaotic patterns are identified using the RK4 method. The chaotic nature of perturbed system is discussed through Lyapunov exponent analysis. Sensitivity and multistability analysis are conducted, considering various initial conditions. The results acquired emphasize the efficacy of the methodologies used in evaluating solitons and phase plots across a broader spectrum of nonlinear models.

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“…Substantial investigations have previously explored the behavior of solitons, utilizing various nonlinear frameworks like the Sakovich equation [13], Schrödinger equation [14], and Zakharov-Kuznetsov modified equal-width equation [15]. The integrable equations in (3 + 1) dimensions have been the subject of increased research attention lately.…”

Section: Introductionmentioning

confidence: 99%

Analyzing Dynamics: Lie Symmetry Approach to Bifurcation, Chaos, Multistability, and Solitons in Extended (3 + 1)-Dimensional Wave Equation

Riaz,

Jhangeer,

Duraihem

et al. 2024

Symmetry

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The examination of new (3 + 1)-dimensional wave equations is undertaken in this study. Initially, the identification of the Lie symmetries of the model is carried out through the utilization of the Lie symmetry approach. The commutator and adjoint table of the symmetries are presented. Subsequently, the model under discussion is transformed into an ordinary differential equation using these symmetries. The construction of several bright, kink, and dark solitons for the suggested equation is then achieved through the utilization of the new auxiliary equation method. Subsequently, an analysis of the dynamical nature of the model is conducted, encompassing various angles such as bifurcation, chaos, and sensitivity. Bifurcation occurs at critical points within a dynamical system, accompanied by the application of an outward force, which unveils the emergence of chaotic phenomena. Two-dimensional plots, time plots, multistability, and Lyapunov exponents are presented to illustrate these chaotic behaviors. Furthermore, the sensitivity of the investigated model is executed utilizing the Runge–Kutta method. This analysis confirms that the stability of the solution is minimally affected by small changes in initial conditions. The attained outcomes show the effectiveness of the presented methods in evaluating solitons of multiple nonlinear models.

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A family of nonlinear Schrodinger equations and their solitons solutions

Cited by 28 publications

References 105 publications

Fractional Laplacian Spinning Particle in External Electromagnetic Field

Fractional Laplacian Spinning Particle in External Electromagnetic Field

Unveiling multi-wave patterns: dynamic characterization and sensitivity analysis of the Yu-Toda-Sasa-Fukuyama model in lattice and liquid

Analyzing Dynamics: Lie Symmetry Approach to Bifurcation, Chaos, Multistability, and Solitons in Extended (3 + 1)-Dimensional Wave Equation

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