Analytical and numerical investigation for Kadomtsev–Petviashvili equation arising in plasma physics

Alharbi, Abdulghani; Almatrafi, M. B.; Abdelrahman, Mahmoud A. E.

doi:10.1088/1402-4896/ab6ce4

Cited by 36 publications

(8 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The criteria for the stability of traveling wave solutions are discussed here for the system (1) at particular intervals. For more details about the stability of the exact solutions, we refer to [37][38][39] and references therein.…”

Section: Stability Analysismentioning

confidence: 99%

Fundamental Solutions for the Coupled KdV System and Its Stability

2020

Self Cite

View full text Add to dashboard Cite

In this paper, we establish exact solutions for the non-linear coupled KdV equations. The exp-function method is used to construct the solitary travelling wave solutions for these equations. The numerical adaptive moving mesh PDEs (MMPDEs) method is also implemented in order to solve the proposed coupled KdV equations. The achieved results may be applicable to some plasma environments, such as ionosphere plasma. Some numerical simulations compared with the exact solutions are provided to illustrate the validity of the proposed methods. Furthermore, the modulational instability is analyzed based on the standard linear-stability analysis. The depiction of the techniques are straight, powerful, robust and can be applied to other nonlinear systems of partial differential equations.

show abstract

Section: Stability Analysismentioning

confidence: 99%

Fundamental Solutions for the Coupled KdV System and Its Stability

2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…Fluid dynamics has been seen as the studies of the underlying mechanisms of liquids, gases or plasmas, and the forces on them, and applied to oceanography, astrophysics, meteorology and biomedical engineering [1,2]. Plasma physics has been considered as the studies of charged particles and fluids interacting with self-consistent electric and magnetic fields, and applied to astrophysics, controlled fusion, accelerator physics and beam storage [3,4]. Nonlinear evolution equations (NLEEs) have been used to describe the nonlinear phenomena in nonlinear optics, fluid dynamics, plasma physics and condensed matter physics [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Bilinear Bäcklund transformation, soliton and breather solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid dynamics and plasma physics

et al. 2021

View full text Add to dashboard Cite

A (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid dynam-ics and plasma physics is hereby investigated. Via the Hirota method, bilinear Bäcklund transformation are obtained, along with two types of the analytic solutions. Kink-shaped soliton solutions are derived via the Hirota method. Breather solutions are derived via the extended homoclinic test approach and lump solutions are obtained from the breather solutions under a limiting procedure. We find that the shape and amplitude of the one-kink soliton keep unchanged during the propagation and the velocity of the one-kink soliton depends on all the coefficients in the equation. We graphically demonstrate that the interaction between the two-kink solitons is elastic, and analyse the solitons with the influence of the coefficients. We observe that the amplitudes and shapes of the breather and lump remain unchanged during the propagation, and graphically present the breathers and lumps with the influence of the coefficients in the equation.

show abstract

“…Investigating both the analytical and numerical results for a given nonlinear partial differential equations (NLPDEs) performs a remarkable role in the explanation of complex phenomena in biology, economy, engineering, mathematical, signal processing, ocean engineering, optics, fluid mechanics, plasma physics, and chemical physics (Alharbi & Almatrafi, 2020a;Alharbi & Almatrafi, 2020b;Alharbi, Almatrafi, & Abdelrahman, 2020;Seadawy, Iqbal, & Lu, 2019). Thus, various vital approaches for determining the solutions of PDEs have been vastly suggested and presented.…”

Section: Introductionmentioning

confidence: 99%

New exact and numerical solutions for the KdV system arising in physical applications

Almatrafi

Alharbi

Abdelrahman

2021

Arab Journal of Basic and Applied Sciences

View full text Add to dashboard Cite

The Kortweg-de Vries (KdV) equation is more appropriate to simulate some natural phenomena and gives more accurate results for some physical systems such as the movement of water waves. In this work, novel analytical traveling wave solutions for a nonlinear KdV system are explored using the sech method. The exact solutions are presented in the form of hyperbolic functions. These solutions show the propagation of water waves on the surface. We also implement the numerical adaptive moving technique (MMPDEs) to construct the relevant system's numerical solutions. A detailed comparison between the numerical and analytical solutions is also presented to confirm the accuracy of the numerical technique. We present some new 2D and 3D figures to illustrate the behaviour of the exact and numerical solutions. The obtained numerical solutions verify the accuracy of the considered methods qualitatively and quantitatively. The stability of the obtained solutions is investigated using the Hamiltonian system. The achieved results can be applied for some new observations in the ocean, coastal water, macroscopic phenomena, and processes. The proposed techniques are potent tools to solve many other non-linear partial differential equations in applied mathematics.

show abstract

Analytical and numerical investigation for Kadomtsev–Petviashvili equation arising in plasma physics

Cited by 36 publications

References 40 publications

Fundamental Solutions for the Coupled KdV System and Its Stability

Fundamental Solutions for the Coupled KdV System and Its Stability

Bilinear Bäcklund transformation, soliton and breather solutions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in fluid dynamics and plasma physics

New exact and numerical solutions for the KdV system arising in physical applications

Contact Info

Product

Resources

About