MDPI - Publisher of Open Access Journals

22 pages, 1071 KiB

Open AccessArticle

Construction of Solitary Wave Solutions to the (3 + 1)-Dimensional Nonlinear Extended and Modified Quantum Zakharov–Kuznetsov Equations Arising in Quantum Plasma Physics

by Mounirah Areshi, Aly R. Seadawy, Asghar Ali, Abdulrahman F. AlJohani, Weam Alharbi and Amal F. Alharbi

Symmetry 2023, 15(1), 248; https://doi.org/10.3390/sym15010248 - 16 Jan 2023

Cited by 13 | Viewed by 2662

Abstract

Several types of solitary wave solutions of (3 + 1)-dimensional nonlinear extended and modified quantum Zakharov–Kuznetsov equations are established successfully via the implantation of three mathematical methods. The concerned models have many fruitful applications to describe the waves in quantum electron–positron–ion magnetoplasmas and weakly nonlinear ion-acoustic waves in plasma. The derived results via the MEAEM method, ESE method, and modified F-expansion have been retrieved and will be expedient in the future to illuminate the collaboration between lower nonlinear ion-acoustic waves. For the physical behavior of the models, some solutions are plotted graphically in 2D and 3D by imparting particular values to the parameters under the given condition at each solution. Hence explored solutions have profitable rewards in the field of mathematical physics. Full article

(This article belongs to the Special Issue New Trends on the Mathematical Models and Solitons Arising in Real-World Problems)

► Show Figures

Figure 1

29 pages, 19412 KiB

Open AccessArticle

Some Applications of the (G′/G,1/G)-Expansion Method for Finding Exact Traveling Wave Solutions of Nonlinear Fractional Evolution Equations

by Sekson Sirisubtawee, Sanoe Koonprasert and Surattana Sungnul

Symmetry 2019, 11(8), 952; https://doi.org/10.3390/sym11080952 - 26 Jul 2019

Cited by 28 | Viewed by 4535

Abstract

In this paper, the

(G^{'} / G, 1 / G)

In this paper, the

(G^{'} / G, 1 / G)

-expansion method is applied to acquire some new, exact solutions of certain interesting, nonlinear, fractional-order partial differential equations arising in mathematical physics. The considered equations comprise the time-fractional, (2+1)-dimensional extended quantum Zakharov-Kuznetsov equation, and the space-time-fractional generalized Hirota-Satsuma coupled Korteweg-de Vries (KdV) system in the sense of the conformable fractional derivative. Applying traveling wave transformations to the equations, we obtain the corresponding ordinary differential equations in which each of them provides a system of nonlinear algebraic equations when the method is used. As a result, many analytical exact solutions obtained of these equations are expressed in terms of hyperbolic function solutions, trigonometric function solutions, and rational function solutions. The graphical representations of some obtained solutions are demonstrated to better understand their physical features, including bell-shaped solitary wave solutions, singular soliton solutions, solitary wave solutions of kink type, and so on. The method is very efficient, powerful, and reliable for solving the proposed equations and other nonlinear fractional partial differential equations with the aid of a symbolic software package. Full article

► Show Figures

Figure 1

Search Results (2)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI

Saved Queries

Search Filter Reset All

Years

Feature Papers

Subjects

Journals

Article Types

Countries / Regions

Search Results (2)

Further Information

Guidelines

MDPI Initiatives

Follow MDPI