Abstract
Bu yazıda, Burgers denkleminin hiperbolik genelleştirilmesinde mixed-dark, üstel ve tekil çözümleri bulmak için üstel fonksiyon yöntemini kullanıyoruz. Tamamen yeni karışık tekil (mixed singular) ve dark soliton çözümleri elde ediyoruz. Parametrelerin uygun değerleri altında, sonuçların çeşitli boyutsal simülasyonları çizilmiştir. Son olarak, makalemizde yeni bir sonuç sunuyoruz.
Keywords
Üstel fonksiyon metodu Burgers denkleminin hiperbolik genelleştirilmesi mixed-dark ve tekil çözümleri
References
- Arshad, M., Seadawy, A. R., Lu, D., Bright-dark solitary wave solutions of generalized higher-order nonlinear Schrödinger equation and its applications in optics, Journal of Electromagnetic Waves and Applications 31, 1711-1721, (2017).
- Yokus, A., Sulaiman, T. A., Bulut, H., On the analytical and numerical solutions of the Benjamin–Bona–Mahony equation. Optical and Quantum Electronics, 50,1, 31, (2018).
- Arshad, M., Seadawy, A. R., Lu, D., Exact bright-dark solitary wave solutions of the higher-order cubic-quintic nonlinear Schrödinger equation and its stability, Optik 138, 40-49, (2017).
- Baskonus, H. M., Bulut, H., New wave behaviors of the system of equations for the Ion Sound and Langmuir waves, Waves in Random and Complex Media, 26,4, 613-625, (2016).
- Dusunceli, F., Solutions for the Drinfeld-Sokolov equation using an ibsefm method, MSU Journal of Science, 6, 1, 505-510, (2018). doi : 10.18586/msufbd.403217
- Baskonus, H. M., Complex soliton solutions to the Gilson-Pickering model, Axioms, 8, 1, 18, (2019).
- Dusunceli, F., New exponential and complex traveling wave solutions to the Konopelchenko-Dubrovsky model, Advances in Mathematical Physics, 2019, Article ID 7801247, 9, (2019).
- Cattani, C., Sulaiman, T. A., Baskonus, H.M., Bulut, H., Solitons in an inhomogeneous Murnaghan's rod, European Physical Journal Plus, 133, 228, 1-12, (2018).
- Cattani, C., Sulaiman, T. A., Baskonus, H. M., Bulut, H., On the soliton solutions to the Nizhnik-Novikov-Veselov and the Drinfel'd-Sokolov systems, Optical and Quantum Electronics, 50, 3, 138, (2018).
- Ilhan, O. A., Sulaiman, T. A., Bulut, H., Baskonus, H. M., On the New Wave Solutions to a Nonlinear Model Arising in Plasma Physics, European Physical Journal Plus, 133, 27, 1-6, (2018).
- Yel, G., Baskonus, H. M., Bulut, H., Novel archetypes of new coupled Konno–Oono equation by using sine–Gordon expansion method, Optical and Quantum Electronics, 49, 285, 1-10, (2017).
- Ilhan, O. A., Esen, A., Bulut, H., Baskonus, H.M., Singular solitons in the pseudo-parabolic model arising in nonlinear surface waves, Results in Physics, 12, 1712–1715, (2019).
- Ciancio, A., Baskonus, H. M., Sulaiman, T. A., Bulut, H., New structural dynamics of isolated waves via the coupled nonlinear Maccari's System with complex structure, Indian Journal of Physics, 92, 10, 1281–1290, (2018).
- Modanlı, M., Two numerical methods for fractional partial differential equation with nonlocal boundary value problem, Advances in Difference Equations, 2018, 333 (2018).
- Modanlı, M., Difference schemes methods for the fractional order differential equation sense of caputo derivative, International Journal of InnovativeEngineering Applications, 2, 53-56, (2018).
- Vladimirov, V. A., Maczka, C., Exact solutions of generalized Burgers equation describing travelling fronts and their interaction, Reports on Mathematical Physics, 60, 2, 317-328, (2007).
- Makarenko, A. S., Moskalkov, A. S., Levkov, A. S., On blow-up solutions in turbulence, Physics Letters A, 235,4, 391-397, (1997).
- Makarenko, A. S., New differential equation model for hydrodynamics with memory effects, Reports on Mathematical Physics, 46, 183-190, (2000).
Abstract
In this paper, we apply the exponential function method to find mixed-dark, exponential and singular soliton solutions in the hyperbolic generalization of the Burgers equation. We obtain some entirely new mixed singular and dark soliton solutions. Under the suitable values of parameters, various dimensional simulations of results are plotted. Finally, we present a conclusion by giving novelties of paper.
Keywords
Exponential function method Hyperbolic Generalization of the Burgers equation mixed-dark and singular soliton solutions
References
- Arshad, M., Seadawy, A. R., Lu, D., Bright-dark solitary wave solutions of generalized higher-order nonlinear Schrödinger equation and its applications in optics, Journal of Electromagnetic Waves and Applications 31, 1711-1721, (2017).
- Yokus, A., Sulaiman, T. A., Bulut, H., On the analytical and numerical solutions of the Benjamin–Bona–Mahony equation. Optical and Quantum Electronics, 50,1, 31, (2018).
- Arshad, M., Seadawy, A. R., Lu, D., Exact bright-dark solitary wave solutions of the higher-order cubic-quintic nonlinear Schrödinger equation and its stability, Optik 138, 40-49, (2017).
- Baskonus, H. M., Bulut, H., New wave behaviors of the system of equations for the Ion Sound and Langmuir waves, Waves in Random and Complex Media, 26,4, 613-625, (2016).
- Dusunceli, F., Solutions for the Drinfeld-Sokolov equation using an ibsefm method, MSU Journal of Science, 6, 1, 505-510, (2018). doi : 10.18586/msufbd.403217
- Baskonus, H. M., Complex soliton solutions to the Gilson-Pickering model, Axioms, 8, 1, 18, (2019).
- Dusunceli, F., New exponential and complex traveling wave solutions to the Konopelchenko-Dubrovsky model, Advances in Mathematical Physics, 2019, Article ID 7801247, 9, (2019).
- Cattani, C., Sulaiman, T. A., Baskonus, H.M., Bulut, H., Solitons in an inhomogeneous Murnaghan's rod, European Physical Journal Plus, 133, 228, 1-12, (2018).
- Cattani, C., Sulaiman, T. A., Baskonus, H. M., Bulut, H., On the soliton solutions to the Nizhnik-Novikov-Veselov and the Drinfel'd-Sokolov systems, Optical and Quantum Electronics, 50, 3, 138, (2018).
- Ilhan, O. A., Sulaiman, T. A., Bulut, H., Baskonus, H. M., On the New Wave Solutions to a Nonlinear Model Arising in Plasma Physics, European Physical Journal Plus, 133, 27, 1-6, (2018).
- Yel, G., Baskonus, H. M., Bulut, H., Novel archetypes of new coupled Konno–Oono equation by using sine–Gordon expansion method, Optical and Quantum Electronics, 49, 285, 1-10, (2017).
- Ilhan, O. A., Esen, A., Bulut, H., Baskonus, H.M., Singular solitons in the pseudo-parabolic model arising in nonlinear surface waves, Results in Physics, 12, 1712–1715, (2019).
- Ciancio, A., Baskonus, H. M., Sulaiman, T. A., Bulut, H., New structural dynamics of isolated waves via the coupled nonlinear Maccari's System with complex structure, Indian Journal of Physics, 92, 10, 1281–1290, (2018).
- Modanlı, M., Two numerical methods for fractional partial differential equation with nonlocal boundary value problem, Advances in Difference Equations, 2018, 333 (2018).
- Modanlı, M., Difference schemes methods for the fractional order differential equation sense of caputo derivative, International Journal of InnovativeEngineering Applications, 2, 53-56, (2018).
- Vladimirov, V. A., Maczka, C., Exact solutions of generalized Burgers equation describing travelling fronts and their interaction, Reports on Mathematical Physics, 60, 2, 317-328, (2007).
- Makarenko, A. S., Moskalkov, A. S., Levkov, A. S., On blow-up solutions in turbulence, Physics Letters A, 235,4, 391-397, (1997).
- Makarenko, A. S., New differential equation model for hydrodynamics with memory effects, Reports on Mathematical Physics, 46, 183-190, (2000).
Details
| Primary Language | English |
|---|---|
| Journal Section | Research Articles |
| Authors | |
| Publication Date | June 28, 2019 |
| Submission Date | February 7, 2019 |
| Published in Issue | Year 2019 Volume: 21 Issue: 2 |