Burger-Huxley Denkleminin Analitik Çözümlerinin (G′/G, 1/G) Genişleme Tekniği ile Analizi

Münevver Tuz

doi:10.63063/jsat.1682099

TR EN

Burger-Huxley Denkleminin Analitik Çözümlerinin (G′/G, 1/G) Genişleme Tekniği ile Analizi

Öz

Bu çalışmada, Burger-Huxley denkleminin analitik çözümleri (G′/G, 1/G) genişleme yöntemi kullanılarak elde edilmiştir. Bu yöntem, doğrusal olmayan kısmi diferansiyel denklemleri çözmek için etkili bir tekniktir ve burada hem konveksiyon hem de reaksiyon-difüzyon terimlerini içeren Burger-Huxley denklemine uygulanmıştır, deklemin trigonometrik, hiperbolik ve rasyonel tip çözümleri elde edilmiştir. Ayrıca, çözümlere keyfi değerler verilerek 2 ve 3 boyutlu grafikler oluşturulmuştur. Elde edilen çözümler, denklemin fiziksel ve matematiksel yapısını daha iyi anlamaya yardımcı olur ve benzer tipteki diferansiyel denklemleri çözmek için bir rehber görevi görür.

Anahtar Kelimeler

(G′/G , 1/G) genişleme yöntemi , doğrusal olmayan kısmi diferansiyel denklem , dengeleme terimi , analitik çözüm.

References

S. Duran, A. Yokuş, and H. Durur, ‘’Surface wave behavior and refraction simulation on the ocean for the fractional Ostrovsky-Benjamin-Bona-Mahony equation,’’ Modern Physics Letters B, vol. 35, no. 31, p. 2150477, 2021.
S.R. Islam et al., ‘’Stability analysis, phase plane analysis, and isolated soliton solution to the LGH equation in mathematical physics,’’ Open Physics, vol. 21, no.1, p. 20230104, 2023.
D. Kaya, and S.M. El-Sayed, ‘’An application of the decomposition method for the generalized KdV and RLW equations,’’ Chaos Solitons Fractals, vol. 17, no. 5, pp. 869–877, 2003.
S. Tarla, and R. Yilmazer, ‘’Investigation of time-dependent Paraxial Equation with an Analytical Method,’’ Optik, vol. 261, p. 169111, 2022.
J. Wang et al., ‘’Dynamic study of multi-peak solitons and other wave solutions of new coupled KdV and new coupled ZakharovKuznetsov systems with their stability,’’ Journal of Taibah University for Science, vol. 17, no.1, p. 2163872, 2023.
S. Duran, ‘’Breaking theory of solitary waves for the Riemann wave equation in fluid Dynamics,’’ International Journal of Modern Physics B, vol. 35, no.09, p. 2150130, 2021.
U. Younas, et al., ‘’Optical solitons and closed form solutions to the (3+ 1)- dimensional resonant Schrödinger dynamical wave equation,’’ International Journal of Modern Physics B, vol. 34, no. 30, 2050291, 2020.
A.R. Seadawy, ‘’Stability analysis for Zakharov-Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma,’’ Computers & Mathematics with Applications, vol. 67, no.1, pp. 172–180, 2014.
M. Wang, X. Li, and J. Zhang, ‘’The (G'/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,’’ Physics Letters A, vol. 372, no. 4, pp. 417–423, 2008.
S. Duran et al.,’’Refraction simulation of internal solitary waves for the fractional Benjamin Ono equation in fluid Dynamics,’’ Modern Physics Letters B, vol. 35, no.26, p. 2150363, 2021.

A. Yokus et al.,‘’Construction of exact traveling wave solutions of the Bogoyavlenskii equation by (G′/G, 1/G)-expansion and (1/G′)-expansion techniques,’’ Results in Physics, vol. 19, p. 103409, 2020.
J. Wang et al.,’’Dynamic study of multi-peak solitons and other wave solutions of new coupled KdV and new coupled Zakharov Kuznetsov systems with their stability,’’ Journal of Taibah University for Science, vol.17, no.1, p. 2163872, 2023.
L. Li, E. Li, and M. Wang, ‘’The (G′/G, 1/G)-expansion method and its application to travelling wave solutions of the Zakharov equations,’’ Applied Mathematics-A Journal of Chinese Universities, vol. 25, pp. 454-462, 2010.
I. E. Inan, Y. Ugurlu, and M. Inc, ‘’New Applications of the (G′/G, 1/G)-Expansion Method,’’ Acta Physica Polonica A, vol. 128, no. 3, pp. 245-251, 2010.
E. M. E. Zayed, and K. A. E Alurrfi, ‘’The (G′/G, 1/G)-Expansion Method and Its Applications for Solving Two Higher Order Nonlinear Evolution Equations,’’ Mathematıcal Problems in Engıneerıng, p.746538, pp.1-20, 2014.
E. M. E. Zayed, and K. A. E Alurrfi, ‘’The (G′/G, 1/G)-Expansion Method and Its Applications to Find the Exact Solutions of Nonlinear PDEs for Nanobiosciences,’’ Mathematıcal Problems in Engıneerıng, p. 521712, pp. 1-10, 2014.
E. S. Panakhov, K. Tas, and M. Sat, ’’Inverse problem for the quadratic pencil of the Sturm-Liouville equations,’’ In AIP Conference Proceedings, 1648 (1), AIP Publishing, 2015.
X. J. Deng, ‘’Travelling wave solutions for the generalized Burgers–Huxley equation,’’ Applied Mathematics and Computation, vol. 204, pp. 733–737, 2008.
J. M. Burger, "A Mathematical Theory of the Flow of a Compressible Fluid." The Quarterly of Applied Mathematics, vol. 1, no.2, pp. 99–113, 1939.
R. C. Mittal, and R. Jiwari, ‘’Numerical study of Burgers-Huxley equation by differential quadrature method,’’ International Journal of Applied Mathematics and Mechanics, vol. 5, pp. 1–9, 2009.
I. Çelik, ‘’ Haar wavelet method for solving generalized Burgers-Huxley equation, ‘’Arab Journal of Mathematical Sciences, vol. 18, pp. 25–37, 2011.
M. Dehghan, B. N. Saray, and M. Lakestani, ‘’Three methods based on the interpolation scaling functions and the mixed collocation finite difference schemes for the numerical solution of the nonlinear generalized Burgers-Huxley equation,’’ Mathematical and Computer Modelling, vol. 55, pp. 1129–1142, 2011.
A.J. Khattak, ‘’A computational mesh less method for the generalized Burger's-Huxley equation,’’ Applied Mathematical Modelling, vol. 33, no. 9, pp. 3718–3729, 2009.
M. Javidi, ‘’A numerical solution of the generalized Burger's-Huxley equation by spectral collocation method,’’ Applied Mathematics and Computation, vol. 178, no.2, pp. 338–344, 2006.
X. Y. Wang, ‘’Nerve propagation and wall in liquid ceytals,’’ Journal Physics Letters A, vol. 112, no. 8, pp. 402–406, 1985.
X. Y. Wang, Z. S. Zhu, and Y.K. Lu, ‘’Solitary wave solutions of the generalized Burger's-Huxley equation,’’ Journal of Physics A: Mathematical and General, vol. 23, no.3, pp. 271–274, 1990.

Details

Primary Language

Turkish

Subjects

Numerical and Computational Mathematics (Other)

Journal Section

Research Article

Authors

Münevver Tuz ^*
0000-0002-9620-247X
Türkiye

Early Pub Date

June 26, 2025

Publication Date

June 30, 2025

Submission Date

April 23, 2025

Acceptance Date

June 17, 2025

Published in Issue

Year 2025 Volume: 3 Number: 1

DOI

https://doi.org/10.63063/jsat.1682099

IZ

https://izlik.org/JA79WS95TK

IEEE

[1]M. Tuz, “Burger-Huxley Denkleminin Analitik Çözümlerinin (G′/G, 1/G) Genişleme Tekniği ile Analizi”, JSAT, vol. 3, no. 1, pp. 42–49, June 2025, doi: 10.63063/jsat.1682099.

Burger-Huxley Denkleminin Analitik Çözümlerinin (G′/G, 1/G) Genişleme Tekniği ile Analizi

Burger-Huxley Denkleminin Analitik Çözümlerinin (G′/G, 1/G) Genişleme Tekniği ile Analizi

Öz

Anahtar Kelimeler

An Analysis of Analytical Solutions of the Burger-Huxley Equation by (G′/G, 1/G) Expansion Technique

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