Poincare-lighthill-kuo method and symbolic computation

Dai, Shun‐Dong

doi:10.1007/bf02437964

Cited by 4 publications

(1 citation statement)

References 18 publications

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“…2 respectively. The PLK method is and effective perturbation technique used as a powerful tool in treating nonlinear problems, including both the weakly and strongly nonlinear method [74].The PLK method is the combination of stretched and strained coordinates. The extended PLK approach is used to determine the two-sided KdV IA solitons and their associated phase shift.…”

Section: Scalingmentioning

confidence: 99%

Head on collision of multi ion acoustic solitons with arbitrary degenerate electrons

Parveen,

Mahmood,

Majid Mirza

et al. 2024

Phys. Scr.

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This study presents a head-on collision of ion-acoustic (IA) multiple solitons in unmagnetizedquantum plasma with arbitrary degenerate electrons. The two-sided Korteweg-de Vries equationsand phase shift associated with them have been derived using the extended Poincaré-Lighthill-Kuo(PLK) method. Depending on the quantum parameter’s value for the degenerate electrons, it isfound that compressive and rarefactive solitons are formed. In addition, the Hirota bilinear approachis used to investigate the overtaking collision, and the expressions of phase shifts of multi-solitonsinteractions are determined. For a specific range of quantum diffraction, i.e, H < 2 compressionalsolitons propagating with supersonic speed, and for H > 2 the rarefactive solitons travelling withsubsonic speed are found. A new nonlinear structure with a larger amplitude is produced duringthe collision in the interaction region. Graphically, the effects of different plasma parameters suchas quantum diffraction and fugacity on interacting IA solitons structures and their associated phaseshifts are investigated. The results of this study might help us to understand the collision of ion acoustic solitons in an unmagnetized quantum plasma with arbitrary electrons degeneracy whichcan exist in astrophysical or laser plasma environment.

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Section: Scalingmentioning

confidence: 99%

Head on collision of multi ion acoustic solitons with arbitrary degenerate electrons

Parveen,

Mahmood,

Majid Mirza

et al. 2024

Phys. Scr.

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Formation of Optical Fractals by Chaotic Solitons in Coupled Nonlinear Helmholtz Equations

Al-Sawalha,

Noor,

Alqudah

et al. 2024

Fractal Fract

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In the present research work, we construct and examine the self-similarity of optical solitons by employing the Riccati Modified Extended Simple Equation Method (RMESEM) within the framework of non-integrable Coupled Nonlinear Helmholtz Equations (CNHEs). This system models the transmission of optical solitons and coupled wave packets in nonlinear optical fibers and describes transverse effects in nonlinear fiber optics. Initially, a complex transformation is used to convert the model into a single Nonlinear Ordinary Differential Equation (NODE), from which hyperbolic, exponential, rational, trigonometric, and rational hyperbolic solutions are produced. In order to better understand the physical dynamics, we offer several 3D, contour, and 2D illustrations for the independent selections of physical parameter values. These illustrations highlight the graphic behaviour of some optical solitons and demonstrate that, under certain constraint conditions, acquired optical solitons lose their stability when they approach an axis and display periodic-axial perturbations, which lead to the generation of optical fractals. As a framework, the generated optical solitons have several useful applications in the field of telecommunications. Furthermore, our suggested RMESEM demonstrates its use by broadening the spectrum of optical soliton solutions, offering important insights into the dynamics of the CNHEs, and suggesting possible applications in the management of nonlinear models.

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Reliable analysis for obtaining exact soliton solutions of (2+1)-dimensional Chaffee-Infante equation

Iqbal,

Riaz,

Alesemi

et al. 2024

MATH

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<abstract><p>The (2+1)-dimensional Chaffee-Infante equation (CIE) is a significant model of the ion-acoustic waves in plasma. The primary objective of this paper was to establish and examine closed-form soliton solutions to the CIE using the modified extended direct algebraic method (m-EDAM), a mathematical technique. By using a variable transformation to convert CIE into a nonlinear ordinary differential equation (NODE), which was then reduced to a system of nonlinear algebraic equations with the assumption of a closed-form solution, the strategic m-EDAM was implemented. When the resulting problem was solved using the Maple tool, many soliton solutions in the shapes of rational, exponential, trigonometric, and hyperbolic functions were produced. By using illustrated 3D and density plots to evaluate several soliton solutions for the provided definite values of the parameters, it was possible to determine if the soliton solutions produced for CIE are cuspon or kink solitons. Additionally, it has been shown that the m-EDAM is a robust, useful, and user-friendly instrument that provides extra generic wave solutions for nonlinear models in mathematical physics and engineering.</p></abstract>

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Poincare-lighthill-kuo method and symbolic computation

Cited by 4 publications

References 18 publications

Head on collision of multi ion acoustic solitons with arbitrary degenerate electrons

Head on collision of multi ion acoustic solitons with arbitrary degenerate electrons

Formation of Optical Fractals by Chaotic Solitons in Coupled Nonlinear Helmholtz Equations

Reliable analysis for obtaining exact soliton solutions of (2+1)-dimensional Chaffee-Infante equation

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