Research Article
BibTex RIS Cite

LİNEER OLMAYAN OLUŞUM DENKLEMLERİNİN ÜSTEL RASYONEL FONKSİYON METODUYLA ÇÖZÜMÜ

Year 2015, Issue: 034, 9 - 16, 15.06.2015

Melike Kaplan Arzu Akbulut Mehmet Naci Özer

Abstract

Bu çalışmada uygulamalı matematik ve matematiksel fizikte önemli yeri
olan equal width wave (EW) ve regularized long wave (RLW) denklemlerinin
tam çözümlerini bulmak için üstel rasyonel fonksiyon metodu kullanılmıştır.
Elde edilen çözümler, bu metodun uygulanması kolay ve etkili sonuçlar verdiğini
gösterir. Ayrıca parametrelere özel değerler verildiğinde tam çözümlerden
soliter dalga çözümleri elde edilebilir. Makaledeki hesaplamalar maple paket
program yardımıyla yapılmıştır.

Keywords

Tam çözümler üstel rasyonel fonksiyon metodu equal width wave (EW) denklemi regularized long wave (RLW) denklemi

References

  • [1] M. J. Ablowitz, P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform, Cambridge University Press, Cambridge (1990).
  • [2] A.M. Wazwaz, Multiple-soliton solutions for the KP Equation by Hirota’s bilinear method and by the tanh–coth method, Appl. Math. Comput. 190, 1, 633-640 (2007).
  • [3] V.O. Vakhnenko, E.J. Parkes, A.J. Morrison, A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation, Chaos Solitons Fractals, 174, 683-692 (2003)
  • [4] E. Fan, H. Zhang, A note on the homogeneous balance method, Physics Letters A, 246 , 403-406 (1998).
  • [5] E. Yusufoglu, A. Bekir, Exact Solutions of Coupled Nonlinear Evolution Equations, Chaos, Solitons and Fractals, 37, 3, 842-848 (2008).
  • [6] A. M Wazwaz, The extended tanh method for new soliton solutions for many forms of the fifth-order KdV equations, Applied Mathematics and Computation, 184, 1002-1014 (2007).
  • [7] S. A. Khuri, A complex tanh-function method applied to nonlinear equations of Schrödinger type, Chaos, Solitons and Fractals, 20, 5, 1037-1040 (2004).
  • [8] A. Bekir, New solitons and periodic wave solutions for some nonlinear physical models by using the sine–cosine method, Physica Scripta, 77, 4, 501-504 (2008).
  • [9] S. Zhang, The periodic wave solutions for the (2 + 1)-dimensional Konopelchenko–Dubrovsky equations, Chaos Solitons Fractals 30, 1213–1220 (2006).
  • [10] M. Inc, M. Ergut, Periodic wave solutions for the generalized shallow water wave equation by the improved Jacobi elliptic function method, Appl. Math. E-Notes 5 (2005) 89–96.
  • [11] E. Yusufoglu, A. Bekir, A travelling wave solution to the Ostrovsky equation, Applied Mathematics and Computation, 186, 1, 256–260 (2007).
  • [12] A. Boz, A. Bekir, Application of Exp-function method for (3+1)-dimensional nonlinear evolution equations, Computers & Mathematics with Applications 56, 5, 1451-1456 (2008).
  • [13] A. Bekir, Application of the (G^'/G)-expansion method for nonlinear evolution equations, Physics Letters A, 372, 19, 3400-3406 (2008).
  • [14] X. L. Li, E. Q. Li, M. L. Wang, The (G^'/G,1/G)-expansion method and its application to travelling wave solutions of the Zakharov equations, Appl. Math. J. Chinese Univ. 25 454-462 (2010).
  • [15] A. Yokus, Bazı Özel Lineer Olmayan Diferensiyel Denklemlerin Çözümlerinin Elde Edilmesi ve Bu Çözümlerin Karşılaştırılması, Doktora Tezi, Fırat Üniversitesi Fen Bilimleri Enstitüsü (2011).
  • [16] M. Kaplan, Lineer Olmayan Schrödinger Denkleminin Tam Çözümleri, Yüksek Lisans Tezi, Eskişehir Osmangazi Üniversitesi Fen Bilimleri Enstitüsü (2013).
  • [17] F. Tascan, A. Bekir, M. Koparan, Travelling wave solutions of nonlinear evolution equations by using the first integral method, Communications in Nonlinear Science and Numerical Simulation, 14, 1810-1815 (2009).
  • [18] Y. Gurefe, A. Sonmezoglu, E. Misirli, Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics, Journal of Physics: Indian Academy of Sciences, 77, 6, 1023–1029 (2011).
  • [19] O. Guner, A. Bekir, Topological (dark) soliton solutions for the Camassa–Holm type equations, Ocean Engineering, 74, 276-279 (2013).
  • [20] J. I. Ramos, Explicit finite difference methods for the EW and RLW equations, Applied Mathematics and Computation, 179, 622–638 (2006).
  • [21] A. Bekir, E. Yusufoglu, Numerical simulation of equal-width wave equation, Computers & Mathematics with Applications, 54, 7-8, 1147–1153 (2007).
  • [22] A. Bekir, E. Yusufoglu, Application of the variational iteration method to the regularized long wave equation, Computers & Mathematics with Applications, 54, 7-8, 1154–1161 (2007).

Year 2015, Issue: 034, 9 - 16, 15.06.2015

Melike Kaplan Arzu Akbulut Mehmet Naci Özer

Abstract

In the study, exponential rational function method is used to construct
exact solutions of the equal width wave (EW) and regularized long
wave (RLW) equations in applied mathematics and mathematical physics. The
exact solutions obtained by the proposed method indicate that the approach is
easy to implement and computationally very challenging. Also we can see that
when the parameters are assigned special values, solitary wave solutions can be
obtained from the exact solutions. All calculations in this paper have been
made with the aid of the Maple packet program.

Keywords

Exact solutions exponential rational function method equal width wave (EW) equation regularized long wave (RLW) equation

References

  • [1] M. J. Ablowitz, P.A. Clarkson, Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform, Cambridge University Press, Cambridge (1990).
  • [2] A.M. Wazwaz, Multiple-soliton solutions for the KP Equation by Hirota’s bilinear method and by the tanh–coth method, Appl. Math. Comput. 190, 1, 633-640 (2007).
  • [3] V.O. Vakhnenko, E.J. Parkes, A.J. Morrison, A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation, Chaos Solitons Fractals, 174, 683-692 (2003)
  • [4] E. Fan, H. Zhang, A note on the homogeneous balance method, Physics Letters A, 246 , 403-406 (1998).
  • [5] E. Yusufoglu, A. Bekir, Exact Solutions of Coupled Nonlinear Evolution Equations, Chaos, Solitons and Fractals, 37, 3, 842-848 (2008).
  • [6] A. M Wazwaz, The extended tanh method for new soliton solutions for many forms of the fifth-order KdV equations, Applied Mathematics and Computation, 184, 1002-1014 (2007).
  • [7] S. A. Khuri, A complex tanh-function method applied to nonlinear equations of Schrödinger type, Chaos, Solitons and Fractals, 20, 5, 1037-1040 (2004).
  • [8] A. Bekir, New solitons and periodic wave solutions for some nonlinear physical models by using the sine–cosine method, Physica Scripta, 77, 4, 501-504 (2008).
  • [9] S. Zhang, The periodic wave solutions for the (2 + 1)-dimensional Konopelchenko–Dubrovsky equations, Chaos Solitons Fractals 30, 1213–1220 (2006).
  • [10] M. Inc, M. Ergut, Periodic wave solutions for the generalized shallow water wave equation by the improved Jacobi elliptic function method, Appl. Math. E-Notes 5 (2005) 89–96.
  • [11] E. Yusufoglu, A. Bekir, A travelling wave solution to the Ostrovsky equation, Applied Mathematics and Computation, 186, 1, 256–260 (2007).
  • [12] A. Boz, A. Bekir, Application of Exp-function method for (3+1)-dimensional nonlinear evolution equations, Computers & Mathematics with Applications 56, 5, 1451-1456 (2008).
  • [13] A. Bekir, Application of the (G^'/G)-expansion method for nonlinear evolution equations, Physics Letters A, 372, 19, 3400-3406 (2008).
  • [14] X. L. Li, E. Q. Li, M. L. Wang, The (G^'/G,1/G)-expansion method and its application to travelling wave solutions of the Zakharov equations, Appl. Math. J. Chinese Univ. 25 454-462 (2010).
  • [15] A. Yokus, Bazı Özel Lineer Olmayan Diferensiyel Denklemlerin Çözümlerinin Elde Edilmesi ve Bu Çözümlerin Karşılaştırılması, Doktora Tezi, Fırat Üniversitesi Fen Bilimleri Enstitüsü (2011).
  • [16] M. Kaplan, Lineer Olmayan Schrödinger Denkleminin Tam Çözümleri, Yüksek Lisans Tezi, Eskişehir Osmangazi Üniversitesi Fen Bilimleri Enstitüsü (2013).
  • [17] F. Tascan, A. Bekir, M. Koparan, Travelling wave solutions of nonlinear evolution equations by using the first integral method, Communications in Nonlinear Science and Numerical Simulation, 14, 1810-1815 (2009).
  • [18] Y. Gurefe, A. Sonmezoglu, E. Misirli, Application of the trial equation method for solving some nonlinear evolution equations arising in mathematical physics, Journal of Physics: Indian Academy of Sciences, 77, 6, 1023–1029 (2011).
  • [19] O. Guner, A. Bekir, Topological (dark) soliton solutions for the Camassa–Holm type equations, Ocean Engineering, 74, 276-279 (2013).
  • [20] J. I. Ramos, Explicit finite difference methods for the EW and RLW equations, Applied Mathematics and Computation, 179, 622–638 (2006).
  • [21] A. Bekir, E. Yusufoglu, Numerical simulation of equal-width wave equation, Computers & Mathematics with Applications, 54, 7-8, 1147–1153 (2007).
  • [22] A. Bekir, E. Yusufoglu, Application of the variational iteration method to the regularized long wave equation, Computers & Mathematics with Applications, 54, 7-8, 1154–1161 (2007).
There are 22 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Melike Kaplan This is me

Arzu Akbulut This is me

Mehmet Naci Özer

Publication Date June 15, 2015
Published in Issue Year 2015 Issue: 034

Cite

APA Kaplan, M., Akbulut, A., & Özer, M. N. (2015). LİNEER OLMAYAN OLUŞUM DENKLEMLERİNİN ÜSTEL RASYONEL FONKSİYON METODUYLA ÇÖZÜMÜ. Journal of Science and Technology of Dumlupınar University(034), 9-16.
 Download Cover Image

HAZİRAN 2020'den itibaren Journal of Scientific Reports-A adı altında ingilizce olarak yayın hayatına devam edecektir.