Öz
Bu araştırmada, van der Waals modelinin bazı tam çözümlerini bulmak için modifiye edilmiş deneme denklem metodu (MEDDM) ele alınmıştır. Van der Waals modelinin çözümünün bulunmasına ek olarak, bu metod lineer olmayan problemlerin çözümünde de kullanılabilir. Böylece çeşitli durumlar için bazı dalga çözümleri elde edilir. Ayrıca, elde edilen çözümlerin fiziksel davranışlarını analiz etmek için Mathematica9 yardımıyla üç ve iki boyutlu grafikler bulunmuştur.
Anahtar Kelimeler
Modifiye edilmiş deneme denklem metodu Van der Waals model Dalga çözümü Tam çözüm
Kaynakça
- Abourabia , A.M., Morad, A.M., 2015. Exact traveling wave solutions of the van der Waals normal form for fluidized granular matter, Physica A: Statistical Mechanics and its Applications, 437, 333-350.
- Argentina, M., Clerc, M.G., Soto, R., 2002. van der Waals–Like Transition in Fluidized Granular Matter, Physical Review Letters, 89, 044301-4.
- Bibi, S., Ahmed, N., Khan, U., Mohyud-Din, S.T., 2018. Some new exact solitary wave solutions of the van der Waals model arising in nature, Results in Physics, 9, 648–655.
- Bulut, H., Baskonus, H.M., Pandir, Y., 2013. The modified trial equation method for fractional wave equation and time fractional generalized Burgers equation, Abstract and Applied Analysis, 2013, 1-8.
- Bulut, H., Pandir, Y., 2013. Modified trial equation method to the nonlinear fractional Sharma-Tasso-Olever equation, International Journal of Modeling and Optimization, 3, 353–357.
- Fan, E., Zhang, H., 1998. A note on the homogeneous balance method, Physics Letters A, 246, 403–406.
- Gurefe, Y., Misirli, E., Sonmezoglu, A., Ekici, M., 2013. Extended trial equation method to generalized nonlinear partial differential equations, Applied Mathematics and Computation, 219, 5253–5260.
- He, J.H., Wu, X.H., 2006. Exp-function method for nonlinear wave equations, Chaos, Solitons and Fractals, 30, 700–708.
- Hirota, R., 2004. The Direct Method in Soliton Theory, 3, Cambridge, 252 – 253.
- Kudryashov, N.A, 2012. One method for finding exact solutions of nonlinear differential equations, Communications in Nonlinear Science and Numerical Simulation, 17, 2248–2253.
- Kumar, R., Kaushal, R.S., Prasad, A., 2010. Solitary wave solutions of selective nonlinear diffusion-reaction equations using homogeneous balance method, Pramana-Journal of Physics, 75, 607–616.
- Lu, D., Seadawy, A.R., Khater, M.A., 2017. Bifurcations of new multi soliton solutions of the van der Waals normal form for fluidized granular matter via six different methods, Results in Physics, 7, 2028-2035.
- Ma, W.X., Xia, T., 2013. Pfaffianized systems for a generalized Kadomtsev-Petviashvili equation, Physica Scripta, 87, 1-8.
- Malfliet, W., Hereman, W., 1996. The tanh method: I. exact solutions of nonlinear evolution and wave equations, Physica Scripta, 54, 563–568.
- Miura, R.M., 1989. Bäcklund Transformation, Berlin, Springer, Germany, 295.
- Odabasi, M., Misirli, E., 2018. On the solutions of the nonlinear fractional differential equations via the Modified Trial Equation Method, Mathematical Methods in the Applied Sciences, 41, 904–911.
- Pandir, Y., Gurefe, Y., Misirli, E., 2012. A new approach to Kudryashov’s method for solving some nonlinear physical models, International Journal of Physical Sciences, 7, 2860–2866.
- Parkes, E.J., Duffy, B.R., 1996. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations, Computer Physics Communications, 98, 288–300.
- Wazwaz, A.M., 2004. A sine-cosine method for handling nonlinear wave equations, Mathematical and Computer Modelling, 40, 499–508.
- Yan, C., 1996. A simple transformation for nonlinear waves, Physics Letters A, 224, 77–84.
- Zafar, B., Khalid, B., Fahand, A., Rezazadeh, H., Bekir, A., 2020. Analytical Behaviour of Travelling Wave Solutions to the Van der Waals Model, International Journal of Applied and Computational Mathematics, 6, 2-16.
- Zhang, S., 2007. Application of Exp-function method to a KdV equation with variable coefficients, Physics Letters A, 365, 448–453.
- Zhao, X., Tang, D., 2002. A new note on a homogeneous balance method, Physics Letters A, 297, 59–67.
Öz
In this research, the modified trial equation method (MTEM) is considered in order to find some exact solutions of the van der Waals model. In addition, to finding the solution of the van der Waals model this method can be used in the solution of nonlinear problems. Thus, some wave solutions for various situations are obtained. Also, three and two dimensional graphs were found with the help of Mathematica9 to analyze the physical behavior of the obtained solutions.
Anahtar Kelimeler
Modified trial equation method Van der Waals model Wave solution Exact solution
Kaynakça
- Abourabia , A.M., Morad, A.M., 2015. Exact traveling wave solutions of the van der Waals normal form for fluidized granular matter, Physica A: Statistical Mechanics and its Applications, 437, 333-350.
- Argentina, M., Clerc, M.G., Soto, R., 2002. van der Waals–Like Transition in Fluidized Granular Matter, Physical Review Letters, 89, 044301-4.
- Bibi, S., Ahmed, N., Khan, U., Mohyud-Din, S.T., 2018. Some new exact solitary wave solutions of the van der Waals model arising in nature, Results in Physics, 9, 648–655.
- Bulut, H., Baskonus, H.M., Pandir, Y., 2013. The modified trial equation method for fractional wave equation and time fractional generalized Burgers equation, Abstract and Applied Analysis, 2013, 1-8.
- Bulut, H., Pandir, Y., 2013. Modified trial equation method to the nonlinear fractional Sharma-Tasso-Olever equation, International Journal of Modeling and Optimization, 3, 353–357.
- Fan, E., Zhang, H., 1998. A note on the homogeneous balance method, Physics Letters A, 246, 403–406.
- Gurefe, Y., Misirli, E., Sonmezoglu, A., Ekici, M., 2013. Extended trial equation method to generalized nonlinear partial differential equations, Applied Mathematics and Computation, 219, 5253–5260.
- He, J.H., Wu, X.H., 2006. Exp-function method for nonlinear wave equations, Chaos, Solitons and Fractals, 30, 700–708.
- Hirota, R., 2004. The Direct Method in Soliton Theory, 3, Cambridge, 252 – 253.
- Kudryashov, N.A, 2012. One method for finding exact solutions of nonlinear differential equations, Communications in Nonlinear Science and Numerical Simulation, 17, 2248–2253.
- Kumar, R., Kaushal, R.S., Prasad, A., 2010. Solitary wave solutions of selective nonlinear diffusion-reaction equations using homogeneous balance method, Pramana-Journal of Physics, 75, 607–616.
- Lu, D., Seadawy, A.R., Khater, M.A., 2017. Bifurcations of new multi soliton solutions of the van der Waals normal form for fluidized granular matter via six different methods, Results in Physics, 7, 2028-2035.
- Ma, W.X., Xia, T., 2013. Pfaffianized systems for a generalized Kadomtsev-Petviashvili equation, Physica Scripta, 87, 1-8.
- Malfliet, W., Hereman, W., 1996. The tanh method: I. exact solutions of nonlinear evolution and wave equations, Physica Scripta, 54, 563–568.
- Miura, R.M., 1989. Bäcklund Transformation, Berlin, Springer, Germany, 295.
- Odabasi, M., Misirli, E., 2018. On the solutions of the nonlinear fractional differential equations via the Modified Trial Equation Method, Mathematical Methods in the Applied Sciences, 41, 904–911.
- Pandir, Y., Gurefe, Y., Misirli, E., 2012. A new approach to Kudryashov’s method for solving some nonlinear physical models, International Journal of Physical Sciences, 7, 2860–2866.
- Parkes, E.J., Duffy, B.R., 1996. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations, Computer Physics Communications, 98, 288–300.
- Wazwaz, A.M., 2004. A sine-cosine method for handling nonlinear wave equations, Mathematical and Computer Modelling, 40, 499–508.
- Yan, C., 1996. A simple transformation for nonlinear waves, Physics Letters A, 224, 77–84.
- Zafar, B., Khalid, B., Fahand, A., Rezazadeh, H., Bekir, A., 2020. Analytical Behaviour of Travelling Wave Solutions to the Van der Waals Model, International Journal of Applied and Computational Mathematics, 6, 2-16.
- Zhang, S., 2007. Application of Exp-function method to a KdV equation with variable coefficients, Physics Letters A, 365, 448–453.
- Zhao, X., Tang, D., 2002. A new note on a homogeneous balance method, Physics Letters A, 297, 59–67.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Mühendislik |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 30 Nisan 2021 |
| Gönderilme Tarihi | 7 Aralık 2020 |
| Yayımlandığı Sayı | Yıl 2021 Cilt: 21 Sayı: 2 |
