Dergiler / Cankaya University Journal of Science and Engineering / 2012 / Cilt: 9 - Sayı: 1

The Modified (G'/G)-Expansion Method for Exact Solutions of the (3+1)-Dimensional Jimbo-Miwa Equation

Sayfa
1–1
Yayın Tarihi
2012-02-01
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

It is shown that the proposed method with the help of a symbolic computation provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this paper, we successfully modified the (G0/G)-expansion method and as an application proposed to construct exact solutions of the (3+1)-dimensional JimboMiwa equation.
📊
Temel Bulgular & Veri:Each of the obtained solutions, namely the hyperbolic function solutions, the trigonometric function solutions and the rational solutions contain an explicit linear function of the variables in the equation in question.
💡
Sonuç & Katkı:It is shown that the proposed method with the help of a symbolic computation provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Nonlinear evolution equation · Jimbo-Miwa equation · (G0/G)-expansion method

Abstract

In this paper, we successfully modified the (G0/G)-expansion method and as an application proposed to construct exact solutions of the (3+1)-dimensional JimboMiwa equation. Each of the obtained solutions, namely the hyperbolic function solutions, the trigonometric function solutions and the rational solutions contain an explicit linear function of the variables in the equation in question. It is shown that the proposed method with the help of a symbolic computation provides a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

🔖

Bu Makaleye Atıf Yap

ABAZARİ, R. (2012). The Modified (G'/G)-Expansion Method for Exact Solutions of the (3+1)-Dimensional Jimbo-Miwa Equation. Cankaya University Journal of Science and Engineering, Cilt: 9 - Sayı: 1, 1–1. https://ajindex.com/articles/746080

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (15)

  1. G. T. Liu and T. Y. Fan, New applications of developed Jacobi elliptic function expansion methods, Physics Letters A 345 (2005), 161–166
  2. M. J. Ablowitz and H. Segur, Solitons and Inverse Scattering Transform, SIAM, Philadelphia 1981
  3. R. Hirota, The Direct Method in Soliton Theory, Cambridge University Press, Cambridge 2004
  4. M. L. Wang, Exact solutions for a compound KdV-Burgers equation, Physics Letters A 213 (1996), 279–287
  5. J. H. He, The homotopy perturbation method for nonlinear oscillators with discontinuities, Applied Mathematics and Computation 151 (2004), 287–292
  6. Z. Y. Yan, An improved algebra method and its applications in nonlinear wave equations, Chaos, Solitons & Fractals 21 (2004), 1013–1021
  7. G. W. Bluman and S. Kumei, Symmetries and Differential Equations, Springer-Verlag, New York 1989
  8. G. Adomian, Solving Frontier Problems of Physics: The Decomposition Method, Kluwer, Boston 1994
  9. R. Abazari and M. Abazari, Numerical simulation of generalized Hirota-Satsuma coupled KdV equation by RDTM and comparison with DTM, Communications in Nonlinear Science and Numerical Simulation 17 (2012), 619–629
  10. H. Jafari, A. Borhanifar and S. A. Karimi, New solitary wave solutions for the bad Boussinesq and good Boussinesq equations, Numerical Methods for Partial Differential Equations 25 (2009), 1231–1237
  11. A. Borhanifar, M. M. Kabir and L. Maryam Vahdat, New periodic and soliton wave solutions for the generalized Zakharov system and (2+ 1)-dimensional Nizhnik-Novikov-Veselov system, Chaos, Solitons & Fractals 42 (2009), 1646–1654
  12. A. Borhanifar and M. M. Kabir, New periodic and soliton solutions by application of Expfunction method for nonlinear evolution equations, Journal of Computational and Applied Mathematics 229 (2009), 158–167
  13. T. Ozi¸s and ¨ ˙I. Aslan, Exact and explicit solutions to the (3 + 1)-dimensional Jimbo-Miwa equation via the Exp-function method, Physics Letters A 372 (2008), 7011–7015
  14. M. Wang, X. Li and J. Zhang, The ( G'/G)–expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics, Physics Letters A 372 (2008), 417–423
  15. A. Bekir, Application of the ( G'/G )–expansion method for nonlinear evolution equations, Physics Letters A 372 (2008), 3400–3406. [16] ˙I. E. ˙Inan, ( G'/G)-Expansion method for traveling wave solutions of the sixth-order Ramani equation, C¸ ankaya University Journal of Science and Engineering 7 (2010), 51–57. [17]