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In this paper, we study the perturbed nonlinear Schrödinger equation (P-NLSE) representing the propagation of waves and may be regarded as a nonlinear complicated physical model. We use the modified extended Tan hyperbolic function (METhF) approach and the [Formula: see text]-expansion approach to construct some new traveling wave structures. Several solutions have been found including dark soliton, periodic-type solitons, bell-shaped solitons, single bell-shaped solitons. We also show a graphical representation of a number of exact solutions to the dynamical model together with a description of their behavior. The proposed techniques can also be extended to various nonlinear evolution models in mathematical physics and engineering.

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

In this article, the generalized (3+1)-dimensional Korteweg-de Vries-Zakharov-Kuznetsov equation is investigated, which describes the influence of magnetic fields on weak ion-acoustic waves in plasma made up of cool and hot electrons and may be regarded as a nonlinear complicated physical model. To find out some new traveling waves solutions and other exact solutions, the improved $F$-expansion approach and the $\exp(-\phi (\zeta))$-expansion approach is applied to above mentioned nonlinear higher dimensional model. Several solutions have been found, including dark soliton, periodic type solitons, bell shaped solitons, single bell shaped solitons. We also show a graphical representation of a number of exact solutions to the equation, together with a description of their behaviour. The proposed techniques can also be used to solve a range of nonlinear evolution problems in mathematical physics and plasma physics.