(1/G')-Açılım Metodunu Kullanarak Sawada–Kotera Denkleminin Hiperbolik Yürüyen Dalga Çözümleri

Yıl 2019, Cilt: 19 Sayı: 3, 615 - 619, 31.12.2019

Hülya Durur , Asıf Yokuş

https://doi.org/10.35414/akufemubid.559048

Cited By: 10

Öz

Bu çalışmada,
)-açılım metodunu
kullanarak Sawada- Kotera denkleminin (S-K) hiperbolik yürüyen dalga çözümleri
elde edildi. Elde edilen çözümlerdeki parametrelere özel değerler verilerek,
grafikler çizildi. Bu grafikler bilgisayar paket programı kullanılarak sunuldu.
Bu makalede, belirlenen hedefe ulaşmak için )-açılım metodu
uygulandı.
)-açılım metodu lineer
olmayan kısmi diferansiyel denklemlerin yürüyen dalga çözümlerini elde etmede
etkili ve güçlü bir metottur.

Anahtar Kelimeler

(1/G')-açılım metodu, Sawada–Kotera denklemi, Lineer olmayan kısmi diferansiyel denklem, Hiperbolik yürüyen dalga çözümü

Hyperbolic Traveling Wave Solutions for Sawada–Kotera Equation Using (1/G') -Expansion Method

Öz

-expansion method is an
effective and powerful method to obtain the traveling wave solutions of
nonlinear partial differential equations.))-expansion method is
applied to reach the goals set.)-expansion methods. Special
values are given to the parameters in the solutions obtained and graphs are
drawn. These graphs are presented using a computer package program. In this
paper, In this study, we obtain hyperbolic traveling wave solutions of the
Sawada–Kotera equation (S-K), using

Anahtar Kelimeler

(1/G') -Expansion Method, Sawada–Kotera equation, Nonlinear partial differential equation, Hyperbolic traveling wave solution

Kaynakça

• Zhang, S., and Xia, T., 2007. A generalized new auxiliary equation method and its applications to nonlinear partial differential equations. Physics Letters A, 363(5-6), 356-360.Wang, M., Li, X., and Zhang, J., 2008. The -expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Physics Letters A, 372(4), 417-423.Liao, S., 2004. On the homotopy analysis method for nonlinear problems. Applied Mathematics and Computation, 147(2), 499-513.Raslan, K. R., 2008. The first integral method for solving some important nonlinear partial differential equations. Nonlinear Dynamics, 53(4), 281-286. Gurefe, Y., Misirli, E., Sonmezoglu, A., and Ekici, M., 2013. Extended trial equation method to generalized nonlinear partial differential equations. Applied Mathematics and Computation, 219(10), 5253-5260. Yokuş, A., 2015. An expansion method for finding traveling wave solutions to nonlinear pdes. İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi, 27,65-81.
• Liu, W., and Chen, K., 2013. The functional variable method for finding exact solutions of some nonlinear time-fractional differential equations. Pramana, 81(3), 377-384. Daghan, D., and Donmez, O., 2016. Exact Solutions of the Gardner Equation and their Applications to the Different Physical Plasmas. Brazilian Journal of Physics, 46(3), 321–333.Tian, K., and Liu, Q. P., 2009. A supersymmetric Sawada–Kotera equation. Physics Letters A, 373(21), 1807-1810. Saba, F., Jabeen, S., Akbar, H., and Mohyud-Din, S. T., 2015. Modified alternative (G′/G)-expansion method to general Sawada–Kotera equation of fifth-order. Journal of the Egyptian Mathematical Society, 23(2), 416-423.Salas, A., 2008. Some solutions for a type of generalized Sawada–Kotera equation. Applied Mathematics and Computation, 196(2), 812-817. Liu, C., and Dai, Z., 2008. Exact soliton solutions for the fifth-order Sawada–Kotera equation. Applied Mathematics and Computation, 206(1), 272-275.Gómez, C. A., and Salas, A. H.,2010. The variational iteration method combined with improved generalized tanh–coth method applied to Sawada–Kotera equation. Applied Mathematics and Computation, 217(4), 1408-1414. Bilige, S., and Chaolu, T., 2010. An extended simplest equation method and its application to several forms of the fifth-order KdV equation. Applied Mathematics and Computation, 216(11), 3146-3153.Dinarvand, S., Khosravi, S., Doosthoseini, A.,and Rashidi, M. M., 2008. The homotopy analysis method for solving the Sawada–Kotera and Lax’s fifth-order KdV equations. Advances in Theoretical and Applied Mechanics, 1(7), 327-335.Wazwaz, A. M., and Ebaid, A., 2014. A study on couplings of the fifth-order integrable Sawada-Kotera and Lax equations. Rom. J. Phys, 59(5-6), 454-465.Ali, M. Y., Hafez, M. G., Chowdury, M. K. H., and Akter, M. T., 2016. Analytical and Traveling Wave Solutions to the Fifth Order Standard Sawada-Kotera Equation via the Generalized Exp (-Φ (ξ))-Expansion Method. Journal of Applied Mathematics and Physics, 4(02), 262. Aziz, I., and Ahmad, M., 2015. Numerical solution of two-dimensional elliptic PDEs with nonlocal boundary conditions. Computers Mathematics with Applications, 69(3), 180-205. Esen, A., Sulaiman, T. A., Bulut, H., and Baskonus, H. M., 2018. Optical solitons to the space-time fractional (1+1)-dimensional coupled nonlinear Schrödinger equation. Optik, 167, 150-156. Yavuz, M., and Ozdemir, N., 2018. Numerical inverse Laplace homotopy technique for fractional heat equations. Thermal Science, 22(1), 185-194. Yavuz, M., Ozdemir, N., and Baskonus, H. M., 2018. Solutions of partial differential equations using the fractional operator involving Mittag-Leffler kernel. The European Physical Journal Plus, 133(6), 215.