Year 2020, Volume 20 , Issue 4, Pages 582 - 588 2020-09-25

Genişletilmiş Deneme Denklemi Yöntemi ile Kübik Lineer Olmayan Schrödinger Denkleminin Yeni Tam Çözümleri
New Exact Solutions of Cubic Nonlinear Schrödinger Equation by Using Extended Trial Equation Method

Yusuf PANDIR [1] , Tural AĞIR [2]


Bu çalışmada, kısmi türevli diferansiyel denklemlerin tam çözümlerinin elde edilmesine olanak sağlayan genişletilmiş deneme denklem yöntemi incelenmiştir. Önerilen bu yöntem kübik lineer olmayan Schrödinger denklemine uygulanmış ve farklı yeni tam çözümleri elde edilmiştir. Elde edilen bu yeni tam çözümlerin literatürde bulunmayan yeni tam çözümleri olduğunu ifade edebiliriz. Ayrıca, bulunan bu yeni tam çözümlerin fiziksel davranışlarını göstermek için iki ve üç boyutlu grafikleri çizilmiştir.

Bu çalışmada, kısmi türevli diferansiyel denklemlerin tam çözümlerinin elde edilmesine olanak sağlayan genişletilmiş deneme denklem yöntemi incelenmiştir. Önerilen bu yöntem kübik lineer olmayan Schrödinger denklemine uygulanmış ve farklı yeni tam çözümleri elde edilmiştir. Elde edilen bu yeni tam çözümlerin literatürde bulunmayan yeni tam çözümleri olduğunu ifade edebiliriz. Ayrıca, bulunan bu yeni tam çözümlerin fiziksel davranışlarını göstermek için iki ve üç boyutlu grafikleri çizilmiştir.

In this study, the extended trial equation method, which allows to obtain exact solutions of the partial differential equations, is investigated. This proposed method is applied to the cubic nonlinear Schrödinger equation and different new exact solutions are obtained. We can state that these new exact solutions are new exact solutions that are not find in the literature. In addition, two and three dimensional graphics drawn to show the physical behavior of these new exact solutions. 

In this study, the extended trial equation method, which allows to obtain exact solutions of the partial differential equations, is investigated. This proposed method is applied to the cubic nonlinear Schrödinger equation and different new exact solutions are obtained. We can state that these new exact solutions are new exact solutions that are not find in the literature. In addition, two and three dimensional graphics drawn to show the physical behavior of these new exact solutions. 

  • Ablowitz, M.J., Prinari, B. and Trubatch, A.D., 2004. Discrete and Continuous Nonlinear Schrödinger Systems, Cambridge Univ. Press.
  • Akbar, M.A., Ali, N.H.M. and Mohyud-Din, S.T., 2013. The modified alternative -expansion method to nonlinear evolution equation: application to the (1+1)-dimensional Drinfel’d-Sokolov-Wilson equation. SpringerPlus, 327, 2-16.
  • Chand, F. and Malik, A.K., 2012. Exact traveling wave solutions of some nonlinear equations using -expansion method. International Journal of Nonlinear Science, 14(4), 416-424.
  • Gurefe, Y., Sonmezoglu A. and Misirli, E., 2011. Application of trial equation method to the nonlinear partial differential equations arising in mathematical physics. Pramana-Journal of Physics, 77(6), 1023-1029.
  • Gurefe, Y., Sonmezoglu A. and Misirli, E., 2012. Application of an irrational trial equation method to high dimensional nonlinear evolution equations. Journal of Advanced Mathematical Studies, 5(1), 41-47.
  • 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.
  • Hietarinta, J., 1997. Hirota's bilinear method and its generalization. International Journal of Modern Physics A, 12(1), 43-51.
  • Imanli, M.I., 2006. Nonlinear Schrödinger equations in homogenous space. MSc thesis, Fırat University, Elazig.
  • Kaplan, M., Ünsal, Ö. and Bekir, A., 2016. Exact solutions of nonlinear Schrödinger equation by using symbolic computation. Mathematical Methods in the Applied Science, 39, 2093-2099.
  • Liu, C.S., 2006. Trial equation method for nonlinear evolution equations with rank inhomogeneous: mathematical discussions and applications. Communications in Theoretical Physics, 45(2), 219-223.
  • Liu, C.S., 2010. Applications of complete discrimination system for polynomial for classifications of traveling wave solutions to nonlinear differential equations. Computer Physics Communications, 181(2), 317-324.
  • Pandir, Y., Gurefe, Y., Kadak, U. and Misirli, E., 2012. Classifications of exact solutions for some nonlinear partial differential equations with generalized evolution. Abstract and Applied Analysis, 2012, Article ID 478531, 16 pp.
  • Pandir, Y., Gurefe, Y. and Misirli, E. 2013. Classification of exact solutions to the generalized Kadomtsev-Petviashvili equation. Physica Scripta, 87(2), 025003, 12 pp.
  • Pandir Y., 2014. Symmetric Fibonacci function solutions of some nonlinear partial differential equations. Applied Mathematics & Information Science, 8, 2237-2241.
  • Pashaev, O. and Tanoglu, G., 2005. Vector shock soliton and the Hirota bilinear method. Chaos, Solitons & Fractals, 26, 95-105.
  • Shakeel, M. and Mo hyud-Din, S. T., 2015. New G'/G-expansion method and its application to the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZK–BBM) equation. Journal of the Association of Arab Universities for Basic & Applied Science, 18(1), 66-81.
  • Sulem C. and Sulem P.L. 1999. The nonlinear Schrödinger equation self-focusing and wave collapse. Springer, New-York.
  • Tandogan, Y.A., Pandir, Y. and Gurefe, Y., 2013. Solutions of the nonlinear differential equations by use of modified Kudryashov method. Turkish Journal of Mathematics and Computer Science, 1, 54-60.
  • Wang M. L., 1996. Exact solutions for compound KdV-Burgers equations. Physics Letters A, 213, 279-287, 1996.
  • Wazwaz A. M., 2008. A sine-cosine method for handling nonlinear wave equations. Mathematical and Computer Modellling, 40(5-6), 499-508.
Primary Language en
Subjects Engineering
Journal Section Articles
Authors

Orcid: 0000-0003-0274-7901
Author: Yusuf PANDIR (Primary Author)
Institution: BOZOK ÜNİVERSİTESİ
Country: Turkey


Orcid: 0000-0002-1521-7873
Author: Tural AĞIR
Institution: BOZOK ÜNİVERSİTESİ
Country: Turkey


Dates

Application Date : March 27, 2020
Publication Date : September 25, 2020

Bibtex @research article { akufemubid709937, journal = {Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi}, issn = {}, eissn = {2149-3367}, address = {}, publisher = {Afyon Kocatepe University}, year = {2020}, volume = {20}, pages = {582 - 588}, doi = {}, title = {New Exact Solutions of Cubic Nonlinear Schrödinger Equation by Using Extended Trial Equation Method}, key = {cite}, author = {Pandır, Yusuf and Ağır, Tural} }
APA Pandır, Y , Ağır, T . (2020). New Exact Solutions of Cubic Nonlinear Schrödinger Equation by Using Extended Trial Equation Method . Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi , 20 (4) , 582-588 . Retrieved from https://dergipark.org.tr/en/pub/akufemubid/issue/56836/709937
MLA Pandır, Y , Ağır, T . "New Exact Solutions of Cubic Nonlinear Schrödinger Equation by Using Extended Trial Equation Method" . Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 20 (2020 ): 582-588 <https://dergipark.org.tr/en/pub/akufemubid/issue/56836/709937>
Chicago Pandır, Y , Ağır, T . "New Exact Solutions of Cubic Nonlinear Schrödinger Equation by Using Extended Trial Equation Method". Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 20 (2020 ): 582-588
RIS TY - JOUR T1 - New Exact Solutions of Cubic Nonlinear Schrödinger Equation by Using Extended Trial Equation Method AU - Yusuf Pandır , Tural Ağır Y1 - 2020 PY - 2020 N1 - DO - T2 - Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi JF - Journal JO - JOR SP - 582 EP - 588 VL - 20 IS - 4 SN - -2149-3367 M3 - UR - Y2 - 2020 ER -
EndNote %0 Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi New Exact Solutions of Cubic Nonlinear Schrödinger Equation by Using Extended Trial Equation Method %A Yusuf Pandır , Tural Ağır %T New Exact Solutions of Cubic Nonlinear Schrödinger Equation by Using Extended Trial Equation Method %D 2020 %J Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi %P -2149-3367 %V 20 %N 4 %R %U
ISNAD Pandır, Yusuf , Ağır, Tural . "New Exact Solutions of Cubic Nonlinear Schrödinger Equation by Using Extended Trial Equation Method". Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 20 / 4 (September 2020): 582-588 .
AMA Pandır Y , Ağır T . New Exact Solutions of Cubic Nonlinear Schrödinger Equation by Using Extended Trial Equation Method. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2020; 20(4): 582-588.
Vancouver Pandır Y , Ağır T . New Exact Solutions of Cubic Nonlinear Schrödinger Equation by Using Extended Trial Equation Method. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2020; 20(4): 582-588.