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

Yıl: 2019 Cilt: 19 Sayı: 3 Sayfa Aralığı: 615 - 619 Metin Dili: İngilizce DOI: 10.35414/akufemubid.559048 İndeks Tarihi: 01-04-2020

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

Öz:
In this study, we obtain hyperbolic traveling wave solutions of the Sawada–Kotera equation (S-K), using(1/𝐺′)-expansion methods. Special values are given to the parameters in the solutions obtained andgraphs are drawn. These graphs are presented using a computer package program. In this paper, (1/𝐺′)-expansion method is applied to reach the goals set. (1/𝐺′)-expansion method is an effective andpowerful method to obtain the traveling wave solutions of nonlinear partial differential equations.
Anahtar Kelime:

(𝟏/𝑮′)-Açılım Metodunu Kullanarak Sawada–KoteraDenkleminin Hiperbolik Yürüyen Dalga Çözümleri

Öz:
Bu çalışmada, (1/𝐺′)-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 (1/𝐺′)-açılım metodu uygulandı. (1/𝐺′)-açılım metodu lineer olmayan kısmi diferansiyel denklemlerin yürüyen dalga çözümlerini elde etmede etkili ve güçlü bir metottur.
Anahtar Kelime:

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • 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 twodimensional elliptic PDEs with nonlocal boundary conditions. Computers Mathematics with Applications, 69(3), 180-205.
  • 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.
  • Celik, E., Bulut, H., and Baskonus, H. M., 2018. Novel features of the nonlinear model arising in nano-ionic currents throughout microtubules. Indian Journal of Physics, 92(9), 1137-1143.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Liao, S., 2004. On the homotopy analysis method for nonlinear problems. Applied Mathematics and Computation, 147(2), 499-513.
  • Liu, C., and Dai, Z., 2008. Exact soliton solutions for the fifth-order Sawada–Kotera equation. Applied Mathematics and Computation, 206(1), 272-275.
  • Raslan, K. R., 2008. The first integral method for solving some important nonlinear partial differential equations. Nonlinear Dynamics, 53(4), 281-286.
  • Saba, F., Jabeen, S., Akbar, H., and Mohyud-Din, S. T., 2015. Modified alternative (G′/G)-expansion method 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.
  • Sulaiman, T. A., Bulut, H., Yokus, A., and Baskonus, H. M., 2019. On the exact and numerical solutions to the coupled Boussinesq equation arising in ocean engineering. Indian Journal of Physics, 93(5), 647-656.
  • Tian, K., and Liu, Q. P., 2009. A supersymmetric Sawada– Kotera equation. Physics Letters A, 373(21), 1807- 1810.
  • Wang, M., Li, X., and Zhang, J., 2008. The (G′/G)- expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics. Physics Letters A, 372(4), 417-423.
  • 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.
  • 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.
  • Yokuş, A., 2015. An expansion method for finding traveling wave solutions to nonlinear pdes. İstanbul Ticaret Üniversitesi Fen Bilimleri Dergisi, 27,65-81.
  • Yokuş, A., and Durur, H., 2019. Complex hyperbolic traveling wave solutions of Kuramoto-Sivashinsky equation using (1/G') expansion method for nonlinear dynamic theory. Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 21(2), 590-599.
  • 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.
APA DURUR H, Yokuş A (2019). Hyperbolic Traveling Wave Solutions for Sawada–Kotera Equation Using (𝟏/𝑮′)-Expansion Method. , 615 - 619. 10.35414/akufemubid.559048
Chicago DURUR Hülya,Yokuş Asıf Hyperbolic Traveling Wave Solutions for Sawada–Kotera Equation Using (𝟏/𝑮′)-Expansion Method. (2019): 615 - 619. 10.35414/akufemubid.559048
MLA DURUR Hülya,Yokuş Asıf Hyperbolic Traveling Wave Solutions for Sawada–Kotera Equation Using (𝟏/𝑮′)-Expansion Method. , 2019, ss.615 - 619. 10.35414/akufemubid.559048
AMA DURUR H,Yokuş A Hyperbolic Traveling Wave Solutions for Sawada–Kotera Equation Using (𝟏/𝑮′)-Expansion Method. . 2019; 615 - 619. 10.35414/akufemubid.559048
Vancouver DURUR H,Yokuş A Hyperbolic Traveling Wave Solutions for Sawada–Kotera Equation Using (𝟏/𝑮′)-Expansion Method. . 2019; 615 - 619. 10.35414/akufemubid.559048
IEEE DURUR H,Yokuş A "Hyperbolic Traveling Wave Solutions for Sawada–Kotera Equation Using (𝟏/𝑮′)-Expansion Method." , ss.615 - 619, 2019. 10.35414/akufemubid.559048
ISNAD DURUR, Hülya - Yokuş, Asıf. "Hyperbolic Traveling Wave Solutions for Sawada–Kotera Equation Using (𝟏/𝑮′)-Expansion Method". (2019), 615-619. https://doi.org/10.35414/akufemubid.559048
APA DURUR H, Yokuş A (2019). Hyperbolic Traveling Wave Solutions for Sawada–Kotera Equation Using (𝟏/𝑮′)-Expansion Method. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 19(3), 615 - 619. 10.35414/akufemubid.559048
Chicago DURUR Hülya,Yokuş Asıf Hyperbolic Traveling Wave Solutions for Sawada–Kotera Equation Using (𝟏/𝑮′)-Expansion Method. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 19, no.3 (2019): 615 - 619. 10.35414/akufemubid.559048
MLA DURUR Hülya,Yokuş Asıf Hyperbolic Traveling Wave Solutions for Sawada–Kotera Equation Using (𝟏/𝑮′)-Expansion Method. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, vol.19, no.3, 2019, ss.615 - 619. 10.35414/akufemubid.559048
AMA DURUR H,Yokuş A Hyperbolic Traveling Wave Solutions for Sawada–Kotera Equation Using (𝟏/𝑮′)-Expansion Method. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi. 2019; 19(3): 615 - 619. 10.35414/akufemubid.559048
Vancouver DURUR H,Yokuş A Hyperbolic Traveling Wave Solutions for Sawada–Kotera Equation Using (𝟏/𝑮′)-Expansion Method. Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi. 2019; 19(3): 615 - 619. 10.35414/akufemubid.559048
IEEE DURUR H,Yokuş A "Hyperbolic Traveling Wave Solutions for Sawada–Kotera Equation Using (𝟏/𝑮′)-Expansion Method." Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi, 19, ss.615 - 619, 2019. 10.35414/akufemubid.559048
ISNAD DURUR, Hülya - Yokuş, Asıf. "Hyperbolic Traveling Wave Solutions for Sawada–Kotera Equation Using (𝟏/𝑮′)-Expansion Method". Afyon Kocatepe Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 19/3 (2019), 615-619. https://doi.org/10.35414/akufemubid.559048