Abstract
Bu makalede matematiksel model olarak incelenen (2+1)-boyutlu Nizhnik-Novikov-Veselov denkleminin dalga çözümleri modifiye edilmiş üstel fonksiyon metodu (MEFM) kullanılarak elde edilmiştir. Bulunan çözüm fonksiyonları incelendiğinde periyodik fonksiyonlar olan hiperbolik ve trigonometrik fonksiyonların ayrıca rasyonel fonksiyonların da elde edildiği belirlenmiştir. Bulunan matematiksel modelin dalga çözümlerini temsil eden iki boyutlu, üç boyutlu, kontur ve yoğunluk grafikleri uygun parametreler belirlenerek çizilmiştir.
Keywords
(2+1)-boyutlu Nizhnik-Novikov-Veselov denklemi modifiye edilmiş üstel fonksiyon metodu dalga çözümleri
References
- Baskonus H M & Bulut H (2015). On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation function method. Waves in Random and Complex Media 25(4): 720-728
- Bulut H, Akturk T & Gurefe Y (2015). An application of the new function method to the generalized double sinh-Gordon equation. AIP Conference Proceedings 1648(1): 370014
- Bulut H (2017). Application of the modified exponential function method to the Cahn-Allen equation. AIP Conference Proceedings 1798(1): 020033
- Chen Y & Yan Z (2005). New exact solutions of (2+1)-dimensional Gardner equation via the new sine-Gordon equation expansion method. Chaos, Solitons & Fractals 26(2): 399-406
- Du X-H, (2010). An irrational trial equation method and its applications. Pramana - Journal of Physics 75(3): 415-422
- Erdogan F, Sakar M G & Saldır O (2020). A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations. Applied Mathematics and Nonlinear Sciences 5(1): 425-436
- Gurefe Y, Misirli E, Sonmezoglu A & Ekici M (2013). Extended trial equation method to generalized nonlinear partial differential equations. Applied Mathematics and Computation 219(10): 5253-5260
- He J-H & Wu X-H (2006). Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals 30(3): 700-708
- Manukure S, Chowdhury A & Zhou Y (2019). Complexiton solutions to the asymmetric Nizhnik-Novikov-Veselov equation. International Journal of Modern Physics B 33(11): 1950098
- Naher H & Abdullah F A (2013). New approach of (G′G)-expansion method and new approach of generalized (G′G)-expansion method for nonlinear evolution equation. AIP Advances 3(3): 032116
- Nuruddeen R I & Nass A M (2018). Exact solitary wave solution for the fractional and classical GEW-Burgers equations: an application of Kudryashov method. Journal of Taibah University for Science 12(3): 309-314
- Peng Y-Z (2005). A class of doubly periodic wave solutions for the generalized Nizhnik–Novikov–Veselov equation. Physics Letters A 337(1-2): 55-60
- Ren Y-J & Zhang H-Q (2006). A generalized F-expansion method to find abundant families of Jacobi Elliptic Function solutions of the (2+1)-dimensional Nizhnik–Novikov–Veselov equation. Chaos, Solitons and Fractals 27: 959-979
- Sakar M, Yeskindirova M & Saldir O (2020). Numerical investigations to design a novel model based on the fifth order system of Emden-Fowler equations. Theoretical and Applied Mechanics Letters 10(5): 333-342
- Wazwaz A-M (2007). Multiple-soliton solutions for the KP equation by Hirota’s bilinear method and by the tanh–coth method. Applied Mathematics and Computation 190(1): 633-640
- Wazwaz A-M (2010). Multiple soliton solutions for the (2+ 1)-dimensional asymmetric Nizhnik-Novikov-Veselov equation. Nonlinear Analysis: Theory, Methods & Applications 72(3-4): 1314-1318
- Xu G-Q & Deng S-F (2016). Painlevé analysis, integrability and exact solutions for a (2 + 1)-dimensional generalized Nizhnik-Novikov-Veselov equation. The European Physical Journal Plus 131: 385
Abstract
In this article, the wave solutions of the (2+1)-dimensional Nizhnik-Novikov-Veselov equation, which is investigated as a mathematical model, are get by using the modified exponential function method (MEFM). When the solution functions found are analyzed, it is determined that hyperbolic and trigonometric functions, which are periodic functions, are also obtained in their rational functions. Two-dimensional, three-dimensional, contour and density graphs representing the wave solutions of the mathematical model found were plotted by determining appropriate parameters.
Keywords
the (2+1)-dimensional Nizhnik-Novikov-Veselov equation the modified exponential function method the wave solutions
References
- Baskonus H M & Bulut H (2015). On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation function method. Waves in Random and Complex Media 25(4): 720-728
- Bulut H, Akturk T & Gurefe Y (2015). An application of the new function method to the generalized double sinh-Gordon equation. AIP Conference Proceedings 1648(1): 370014
- Bulut H (2017). Application of the modified exponential function method to the Cahn-Allen equation. AIP Conference Proceedings 1798(1): 020033
- Chen Y & Yan Z (2005). New exact solutions of (2+1)-dimensional Gardner equation via the new sine-Gordon equation expansion method. Chaos, Solitons & Fractals 26(2): 399-406
- Du X-H, (2010). An irrational trial equation method and its applications. Pramana - Journal of Physics 75(3): 415-422
- Erdogan F, Sakar M G & Saldır O (2020). A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations. Applied Mathematics and Nonlinear Sciences 5(1): 425-436
- Gurefe Y, Misirli E, Sonmezoglu A & Ekici M (2013). Extended trial equation method to generalized nonlinear partial differential equations. Applied Mathematics and Computation 219(10): 5253-5260
- He J-H & Wu X-H (2006). Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals 30(3): 700-708
- Manukure S, Chowdhury A & Zhou Y (2019). Complexiton solutions to the asymmetric Nizhnik-Novikov-Veselov equation. International Journal of Modern Physics B 33(11): 1950098
- Naher H & Abdullah F A (2013). New approach of (G′G)-expansion method and new approach of generalized (G′G)-expansion method for nonlinear evolution equation. AIP Advances 3(3): 032116
- Nuruddeen R I & Nass A M (2018). Exact solitary wave solution for the fractional and classical GEW-Burgers equations: an application of Kudryashov method. Journal of Taibah University for Science 12(3): 309-314
- Peng Y-Z (2005). A class of doubly periodic wave solutions for the generalized Nizhnik–Novikov–Veselov equation. Physics Letters A 337(1-2): 55-60
- Ren Y-J & Zhang H-Q (2006). A generalized F-expansion method to find abundant families of Jacobi Elliptic Function solutions of the (2+1)-dimensional Nizhnik–Novikov–Veselov equation. Chaos, Solitons and Fractals 27: 959-979
- Sakar M, Yeskindirova M & Saldir O (2020). Numerical investigations to design a novel model based on the fifth order system of Emden-Fowler equations. Theoretical and Applied Mechanics Letters 10(5): 333-342
- Wazwaz A-M (2007). Multiple-soliton solutions for the KP equation by Hirota’s bilinear method and by the tanh–coth method. Applied Mathematics and Computation 190(1): 633-640
- Wazwaz A-M (2010). Multiple soliton solutions for the (2+ 1)-dimensional asymmetric Nizhnik-Novikov-Veselov equation. Nonlinear Analysis: Theory, Methods & Applications 72(3-4): 1314-1318
- Xu G-Q & Deng S-F (2016). Painlevé analysis, integrability and exact solutions for a (2 + 1)-dimensional generalized Nizhnik-Novikov-Veselov equation. The European Physical Journal Plus 131: 385
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Research Articles |
| Authors | |
| Publication Date | June 30, 2021 |
| Submission Date | April 26, 2021 |
| Published in Issue | Year 2021 Volume: 11 Issue: 1 |