Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different Methods

Seydi Battal Gazi Karakoç; Khalid K. Ali; Mona Mehanna

doi:10.32323/ujma.1287524

EN

Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different Methods

Abstract

The Schamel-Korteweg-de Vries (S-KdV) equation including a square root nonlinearity is very important pattern for the research of ion-acoustic waves in plasma and dusty plasma. As known, it is significant to discover the traveling wave solutions of such equations. Therefore, in this paper, some new traveling wave solutions of the S-KdV equation, which arises in plasma physics in the study of ion acoustic solitons when electron trapping is present and also it governs the electrostatic potential for a certain electron distribution in velocity space, are constructed. For this purpose, the Bernoulli Sub-ODE and modified auxiliary equation methods are used. It has been shown that the suggested methods are effective and give different types of function solutions as: hyperbolic, trigonometric, power, exponential, and rational functions. The applied computational strategies are direct, efficient, concise and can be implemented in more complex phenomena with the assistant of symbolic computations. The results found in the paper are of great interest and may also be used to discover the wave sorts and specialities in several plasma systems.

Keywords

Auxiliary equation method, Bernoulli Sub-ODE method, Modified, Schamel--Korteweg--de Vries equation, Travelling wave solutions

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Details

Primary Language

English

Subjects

Applied Mathematics

Journal Section

Research Article

Authors

Seydi Battal Gazi Karakoç ^*
0000-0002-2348-4170
Türkiye

Khalid K. Ali
0000-0002-7801-2760
Egypt

Mona Mehanna
0000-0003-4349-1113
Egypt

Publication Date

July 1, 2023

Submission Date

April 25, 2023

Acceptance Date

June 9, 2023

Published in Issue

Year 2023 Volume: 6 Number: 2

DOI

https://doi.org/10.32323/ujma.1287524

IZ

https://izlik.org/JA88NG53MX

APA

Karakoç, S. B. G., Ali, K. K., & Mehanna, M. (2023). Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different Methods. Universal Journal of Mathematics and Applications, 6(2), 65-75. https://doi.org/10.32323/ujma.1287524

AMA

1.Karakoç SBG, Ali KK, Mehanna M. Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different Methods. Univ. J. Math. Appl. 2023;6(2):65-75. doi:10.32323/ujma.1287524

Chicago

Karakoç, Seydi Battal Gazi, Khalid K. Ali, and Mona Mehanna. 2023. “Exact Traveling Wave Solutions of the Schamel-KdV Equation With Two Different Methods”. Universal Journal of Mathematics and Applications 6 (2): 65-75. https://doi.org/10.32323/ujma.1287524.

EndNote

Karakoç SBG, Ali KK, Mehanna M (July 1, 2023) Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different Methods. Universal Journal of Mathematics and Applications 6 2 65–75.

IEEE

[1]S. B. G. Karakoç, K. K. Ali, and M. Mehanna, “Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different Methods”, Univ. J. Math. Appl., vol. 6, no. 2, pp. 65–75, July 2023, doi: 10.32323/ujma.1287524.

ISNAD

Karakoç, Seydi Battal Gazi - Ali, Khalid K. - Mehanna, Mona. “Exact Traveling Wave Solutions of the Schamel-KdV Equation With Two Different Methods”. Universal Journal of Mathematics and Applications 6/2 (July 1, 2023): 65-75. https://doi.org/10.32323/ujma.1287524.

JAMA

1.Karakoç SBG, Ali KK, Mehanna M. Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different Methods. Univ. J. Math. Appl. 2023;6:65–75.

MLA

Karakoç, Seydi Battal Gazi, et al. “Exact Traveling Wave Solutions of the Schamel-KdV Equation With Two Different Methods”. Universal Journal of Mathematics and Applications, vol. 6, no. 2, July 2023, pp. 65-75, doi:10.32323/ujma.1287524.

Vancouver

1.Seydi Battal Gazi Karakoç, Khalid K. Ali, Mona Mehanna. Exact Traveling Wave Solutions of the Schamel-KdV Equation with Two Different Methods. Univ. J. Math. Appl. 2023 Jul. 1;6(2):65-7. doi:10.32323/ujma.1287524