Some traveling wave solutions to the generalized (3 + 1)‐dimensional Korteweg–de Vries–Zakharov–Kuznetsov equation in plasma physics

Abstract

The generalized Korteweg-de Vries-Zakharov-Kuznetsov model is one of the dominant nonlinear complex structures to exhibit the influence of magnetic fields on weak ion-acoustic waves in plasma made up of cool and hot electrons. In this study, the nonlinear higher dimensional model is subjected to the extended F-expansion approach and the exp(−𝜙(𝜁))-expansion strategy in order to discover some novel traveling waves solutions and other exact solutions. There have been several solutions discovered, such as bright, dark, periodic, bell-shaped, and single bell-shaped wave structures. Furthermore, the stability analysis of the model is also reported along with the dynamical visualization of the charismatic behavior of various solitons with the aid of 3D, 2D, and contour plots. The proposed techniques can also be implemented to analyze a wide range of nonlinear evolution models emerging in diverse disciplines of science and technology including mathematical physics and plasma physics. KEYWORDS exact wave solutions, improved F-expansion method, stability analysis, the (3 + 1)-dimensional gKdV-ZK model, the exp(−𝜙(𝜁 ))-expansion technique, traveling waves solutions MSC CLASSIFICATION

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

“…Since then, the search for the solution of the gKdV-ZK equation and its variations were studied intensively with respect to different methods, such as using the Lie symmetry approach [12], the bilinear transformation-model and the expansion version of the φ 6 method [13], the new modification of the extended direct algebraic method [14], implementing of the fractional direct algebraic methods and the extended direct algebraic method, to present solitary wave solutions. Furthermore, the stability analysis is discussed [15], the extended F-expansion technique and the expansion version of the exp(−φ (F )) approach [16], the first integral method [17], through using Painlevé expansion, the Painlevé--Bäcklund transformations are obtained, and the bilinear forms of (1) have been derived [18]. The Bernoulli sub-ODE approach has been utilized [19].…”