BibTex RIS Cite

The Tanh-coth Method For Two System Of Sobolev Type Equations In Mathematical Physics

Year 2016, Volume: 4 Issue: 1, 52 - 62, 01.05.2016

Abstract

Sobolev equations have been used to describe many physical phenomena and they are characterized by having mixed time and space derivatives appearing in the highest-order terms of an partial differential equation. In this work we consider two important system of Sobolev type equations namely improved Boussinesq and higher-order improved Boussinesq. By using tanh-coth method, we obtain abundant new travelling wave solutions of these important physical structures.

References

  • [1] P. L. Christiansen, P. S. Lomdahl and V. Muto, "On a Toda lattice model with a transversal degree of freedom", Nonlinearity, vol. 4, pp. 477-501, 1991.
  • [2] K. R. Khusnutdinova, A. M. Samsonov and A. S. Zakharov, "Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures", Physical Review E, pp. 1-14, vol. 79, 2009
  • [3] J. A. D. Wattis, "Solitary waves in a diatomic lattice: analytic approximations for a wide range of speeds by quasi-continuum methods", Physics Letters A, vol. 284, pp. 16-22, 2001
  • [4] A. De Godefroy, "Blow up of solutions of a generalized Boussinesq equation", IMA Journal of Applied Mathematics, vol. 60, pp.123-138,1998
  • [5] S. Wang and M. Li, "The Cauchy problem for coupled IMBq equations", IMA Journal of Applied Mathematics, vol. 74 ,pp. 726-740, 2009
  • [6] D. Rosenau, "Dynamics of dense lattice", Phys. Rev. B, vol.36, pp. 5868-5876, 1987

Matematiksel Fizikteki Sobolev Tipi İki Denklem Sistemi için Tanh-Coth Yöntemi

Year 2016, Volume: 4 Issue: 1, 52 - 62, 01.05.2016

Abstract

Sobolov denklemleri en yüksek mertebeden türevinde zaman ve boyuta göre türevleri beraber bulunduran denklemler olarak tanımlanır. Bu çalışmada, Boussinesq ve yüksek mertebeden geliştirilmiş Boussinesq adlı iki önemli Sobolev denklem sistemini ele aldık. Tanh-coth yöntemi kullanarak bu iki önemli denklem sisteminin bir çok yeni hareketli dalga çözümünü elde ettik

References

  • [1] P. L. Christiansen, P. S. Lomdahl and V. Muto, "On a Toda lattice model with a transversal degree of freedom", Nonlinearity, vol. 4, pp. 477-501, 1991.
  • [2] K. R. Khusnutdinova, A. M. Samsonov and A. S. Zakharov, "Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures", Physical Review E, pp. 1-14, vol. 79, 2009
  • [3] J. A. D. Wattis, "Solitary waves in a diatomic lattice: analytic approximations for a wide range of speeds by quasi-continuum methods", Physics Letters A, vol. 284, pp. 16-22, 2001
  • [4] A. De Godefroy, "Blow up of solutions of a generalized Boussinesq equation", IMA Journal of Applied Mathematics, vol. 60, pp.123-138,1998
  • [5] S. Wang and M. Li, "The Cauchy problem for coupled IMBq equations", IMA Journal of Applied Mathematics, vol. 74 ,pp. 726-740, 2009
  • [6] D. Rosenau, "Dynamics of dense lattice", Phys. Rev. B, vol.36, pp. 5868-5876, 1987
There are 6 citations in total.

Details

Other ID JA36PT65RC
Journal Section Research Article
Authors

S. Akçağıl This is me

O. Gözükızıl This is me

Publication Date May 1, 2016
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

APA Akçağıl, S., & Gözükızıl, O. (2016). The Tanh-coth Method For Two System Of Sobolev Type Equations In Mathematical Physics. MANAS Journal of Engineering, 4(1), 52-62.
AMA Akçağıl S, Gözükızıl O. The Tanh-coth Method For Two System Of Sobolev Type Equations In Mathematical Physics. MJEN. May 2016;4(1):52-62.
Chicago Akçağıl, S., and O. Gözükızıl. “The Tanh-Coth Method For Two System Of Sobolev Type Equations In Mathematical Physics”. MANAS Journal of Engineering 4, no. 1 (May 2016): 52-62.
EndNote Akçağıl S, Gözükızıl O (May 1, 2016) The Tanh-coth Method For Two System Of Sobolev Type Equations In Mathematical Physics. MANAS Journal of Engineering 4 1 52–62.
IEEE S. Akçağıl and O. Gözükızıl, “The Tanh-coth Method For Two System Of Sobolev Type Equations In Mathematical Physics”, MJEN, vol. 4, no. 1, pp. 52–62, 2016.
ISNAD Akçağıl, S. - Gözükızıl, O. “The Tanh-Coth Method For Two System Of Sobolev Type Equations In Mathematical Physics”. MANAS Journal of Engineering 4/1 (May 2016), 52-62.
JAMA Akçağıl S, Gözükızıl O. The Tanh-coth Method For Two System Of Sobolev Type Equations In Mathematical Physics. MJEN. 2016;4:52–62.
MLA Akçağıl, S. and O. Gözükızıl. “The Tanh-Coth Method For Two System Of Sobolev Type Equations In Mathematical Physics”. MANAS Journal of Engineering, vol. 4, no. 1, 2016, pp. 52-62.
Vancouver Akçağıl S, Gözükızıl O. The Tanh-coth Method For Two System Of Sobolev Type Equations In Mathematical Physics. MJEN. 2016;4(1):52-6.

Manas Journal of Engineering 

16155