Characteristic of ion-acoustic waves described in the solutions of the (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation

Abstract

The generalized Korteweg-de Varies-Zakharov-Kuznetsov equation (gKdV-ZK) in (3+1)-dimension has been investigated in this research. This model is used to elucidate how a magnetic field affects the weak ion-acoustic wave in the field of plasma physics.To deftly analyze the wide range of wave structures, we utilized the modified extended tanh and the extended rational sinh-cosh methods. Hyperbolic, periodic, and traveling wave solutions are presented as the results. Consequently, solitary wave solutions are also attained. This study shows that the solutions reported here are distinctive when our findings are contrasted against well-known outcomes. Moreover, realized findings are figured out in 3-dimensional, 2-dimensional, and contour profile graphs for the reader to comprehend their dynamics due to parameter selection. According to the findings, we can conclude that the suggested computational techniques are simple, dynamic, and well-organized. These methods are very functional for numerical calculations of complex nonlinear problems. Our results include a fundamental starting point in understanding physical behavior and the structure of the studied systems.

A new approach to the Benjamin-Bona-Mahony equation via ultraspherical wavelets collocation method

“…A lot of mathematicians have also recently introduced several new techniques for solving differential equations, such as the Hermite wavelet technique [4], the Bäcklund transformation method [5], the Fibonacci wavelet scheme for solving hyperbolic PDE, dispersive PDE, the Rosenau-Hyman equation [6][7][8], the first integral method for MBBM equation [9], Hirota's bilinear method [10], Bernoulli wavelet scheme for nonlinear Murray equation [11], BBMB equations by Exp-Function method [12], (2+1) dimensional Sobolev equation via wavelet technique [13], the Haar wavelet method for the BBM equations [14], ultraspherical wavelet scheme for spectral solutions of Riccati equations [15], ultraspherical wavelet technique for solving 2nth-order boundary value problems [16], ultraspherical operational matrices of derivatives [17], clique polynomial and Adomian decomposition method for solving differential equations [18], and Laguerre wavelets scheme for solving delay differential equations [19], Bernoulli wavelet technique for solving biological models [20], explicit solution of atmospheresoil-land plant carbon cycle system [21], study on Kudryashov-Sinelshchikov dynamical equation [22], study on Caudrey-Dodd-Gibbon-Sawada-Kotera partial differential equation [23], structure of the analytic solutions for Schrödinger equation [24], solutions for Konopelchenko-Dubrovsky equation [25], solutions of Kadomtsev-Petviashvili-Benjamin-Bona-Mahony equation [26], solutions of the Korteweg-de Vries-Zakharov-Kuznetsov equation [27].…”