Öz
In this study, we have applied the modified exp -expansion function method (MEFM) to obtain the exact travelling wave solutions for the (3+1) dimensional Khokhlov–Zabolotskaya–Kuznetsov (KZK) equation and (3+1)-dimensional Jimbo-Miwa (JM) equation. Dark soliton solution, dark-bright soliton solution, hyperbolic function solution and trigonometric function solution of the (3+1) dimensional KZK equation and (3+1)-dimensional JM equation have been found by using this method. After that, we have scratched the 2D and 3D graphs for all exact solutions obtained in this study by using Wolfram Mathematica 9. Thus, the graphical simulations openly show force of this method.
Anahtar Kelimeler
The (3+1) dimensional KZK Equation (3+1)-Dimensional Jimbo-Miwa Equation MEFM Dark Soliton Solution Trigonometric Function Solutions Hyperbolic Solutions
Kaynakça
- Akbar, M. A., Mohd. Ali, N., Tanjim, T., 2020. Adequate soliton solutions to the perturbed Boussinesq equation and the KdV-Caudrey-Dodd-Gibbon Equation. Journal of King Saud University – Science, 32, 6, 2777–2785.
- Akcagil, S., Aydemir, T., 2016. New exact solutions for the Khokhlov-Zabolotskaya-Kuznetsov, the Newell-Whitehead-Segel and the Rabinovich wave equations by using a new modification of the tanh-coth method. Cogent Mathematics, 3, 1, 1193104, 1-12.
- Ali, Khalid K., Osman, M.S., Mahmoud Abdel-Aty, 2020. New optical solitary wave solutions of Fokas-Lenells equation in optical fiber via Sine-Gordon expansion method. Alexandria Engineering Journal, 59, 3, 1191–1196.
- Durur, H., Ilhan, E., Bulut, H., 2020. Novel Complex Wave Solutions of the (2+1)-Dimensional Hyperbolic Nonlinear Schrödinger Equation. Fractal and Fractional, 4, 41, 1-8.
- Ismael, H. F., Bulut, H., 2020. Multi soliton solutions, M-lump waves and mixed solution lump solutions to the Sawada-Kotera equation in (2+1) dimensions, Chinese Journal of Physics, In press, 19, 1-8.
- Ismael, H. F., Bulut, H., Park, C., Osman, M.S., 2020. M-lump, N-soliton solutions, and the collision phenomena for the (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation. Results in Physics, 19, 103329, 1-6.
- Rozanova-Pierrat, A., 2006. Mathematical analysis of Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, hal-00112147.
- Tuluce Demiray, S., 2020. New Solitions of Biswas-Arshed equation with beta time Derivative. Optik, 222, 165405, 1-5.
- Tuluce Demiray, S., 2020. New Soliton Solitions of Optical Pulse Envolepe E(Z, τ) with Beta Time Derivative. Optik, 223, 165453, 1-6.
- Tuluce Demiray, S., Bulut, H., 2018. A New Method for (4+1) Dimensional Fokas Equation, ITM Web of Conferences. 22, 01065, 1-5.
- Yokus, A., Kaya, D., 2020. Comparison exact and numerical simulation of the traveling wave solution in nonlinear Dynamics. International Journal of Modern Physics B, 34, 29, 2050282, 1-22.
- Yokus, A., Durur, H., Taher, A. N., Abu-Zinadah, H., Tuz, M., Ahmad, H., 2020. Study on the applications of two analytical methods for the construction of traveling wave solutions of the modified equal width equation. Open Physics, 18, 1, 1003-1010.
- Yokus, A., Durur, H., Ahmad, H., Yao, S. W., 2020. Construction of Different Types Analytic Solutions for the Zhiber-Shabat Equation. Mathematics, 8, 908, 1-16.
- Zayed, E. M. E., Amer, Y. A., Ahmed, H. A., 2013. Functional variable method and its applications for finding exact solutions of nonlinear PDEs in mathematical physics. Scientific Research and Essays, 8, 42, 2068-2074.
- Zhang, S., Sun, Y.N., Ba, J.M., Dong, L., 2009. Explicit and exact solutions with multiple arbitrary analytic functions of Jimbo-Miwa Equation. Applications and Applied Mathematics, 4, 279-289.
- Zheng, X., Xiao, Q., Ouyang, Z., 2021. A smooth soliton solution and a periodic cuspon solution of the Novikov equation. Applied Mathematics Letters, 112, 106786, 1-7.
Öz
Bu çalışmada, (3+1) boyutlu Khokhlov – Zabolotskaya – Kuznetsov (KZK) denklemi ve (3+1) boyutlu Jimbo-Miwa (JM) denklemlerinin yürüyen tam dalga çözümlerini elde etmek için, modifiye edilmiş exp -açılım fonksiyon metodunu (MEFM) uyguladık. Bu yöntemle (3+1) boyutlu KZK denkleminin ve (3+1) boyutlu JM denkleminin dark soliton çözümü, dark-bright soliton çözümü, hiperbolik fonksiyon çözümü ve trigonometrik fonksiyon çözümü bulunmuştur. Daha sonra, bu çalışmada elde edilen tüm kesin çözümler için Wolfram Mathematica 9’u kullanarak 2 boyutlu ve 3 boyutlu grafikleri çizdik. Böylece, grafiksel gösterimler bu yöntemin gücünü açıkça göstermektedir.
Anahtar Kelimeler
(3 + 1) boyutlu KZK Denklemi ; (3 + 1) - Boyutlu Jimbo-Miwa Denklemi; MEFM Dark Soliton Çözümü Trigonometrik Fonksiyon Çözümleri Hiperbolik Çözümler
Kaynakça
- Akbar, M. A., Mohd. Ali, N., Tanjim, T., 2020. Adequate soliton solutions to the perturbed Boussinesq equation and the KdV-Caudrey-Dodd-Gibbon Equation. Journal of King Saud University – Science, 32, 6, 2777–2785.
- Akcagil, S., Aydemir, T., 2016. New exact solutions for the Khokhlov-Zabolotskaya-Kuznetsov, the Newell-Whitehead-Segel and the Rabinovich wave equations by using a new modification of the tanh-coth method. Cogent Mathematics, 3, 1, 1193104, 1-12.
- Ali, Khalid K., Osman, M.S., Mahmoud Abdel-Aty, 2020. New optical solitary wave solutions of Fokas-Lenells equation in optical fiber via Sine-Gordon expansion method. Alexandria Engineering Journal, 59, 3, 1191–1196.
- Durur, H., Ilhan, E., Bulut, H., 2020. Novel Complex Wave Solutions of the (2+1)-Dimensional Hyperbolic Nonlinear Schrödinger Equation. Fractal and Fractional, 4, 41, 1-8.
- Ismael, H. F., Bulut, H., 2020. Multi soliton solutions, M-lump waves and mixed solution lump solutions to the Sawada-Kotera equation in (2+1) dimensions, Chinese Journal of Physics, In press, 19, 1-8.
- Ismael, H. F., Bulut, H., Park, C., Osman, M.S., 2020. M-lump, N-soliton solutions, and the collision phenomena for the (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation. Results in Physics, 19, 103329, 1-6.
- Rozanova-Pierrat, A., 2006. Mathematical analysis of Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation, hal-00112147.
- Tuluce Demiray, S., 2020. New Solitions of Biswas-Arshed equation with beta time Derivative. Optik, 222, 165405, 1-5.
- Tuluce Demiray, S., 2020. New Soliton Solitions of Optical Pulse Envolepe E(Z, τ) with Beta Time Derivative. Optik, 223, 165453, 1-6.
- Tuluce Demiray, S., Bulut, H., 2018. A New Method for (4+1) Dimensional Fokas Equation, ITM Web of Conferences. 22, 01065, 1-5.
- Yokus, A., Kaya, D., 2020. Comparison exact and numerical simulation of the traveling wave solution in nonlinear Dynamics. International Journal of Modern Physics B, 34, 29, 2050282, 1-22.
- Yokus, A., Durur, H., Taher, A. N., Abu-Zinadah, H., Tuz, M., Ahmad, H., 2020. Study on the applications of two analytical methods for the construction of traveling wave solutions of the modified equal width equation. Open Physics, 18, 1, 1003-1010.
- Yokus, A., Durur, H., Ahmad, H., Yao, S. W., 2020. Construction of Different Types Analytic Solutions for the Zhiber-Shabat Equation. Mathematics, 8, 908, 1-16.
- Zayed, E. M. E., Amer, Y. A., Ahmed, H. A., 2013. Functional variable method and its applications for finding exact solutions of nonlinear PDEs in mathematical physics. Scientific Research and Essays, 8, 42, 2068-2074.
- Zhang, S., Sun, Y.N., Ba, J.M., Dong, L., 2009. Explicit and exact solutions with multiple arbitrary analytic functions of Jimbo-Miwa Equation. Applications and Applied Mathematics, 4, 279-289.
- Zheng, X., Xiao, Q., Ouyang, Z., 2021. A smooth soliton solution and a periodic cuspon solution of the Novikov equation. Applied Mathematics Letters, 112, 106786, 1-7.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 24 Şubat 2021 |
| Gönderilme Tarihi | 7 Ocak 2021 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 21 Sayı: 1 |
