Research Article

Soliton solutions of Hirota equation and Hirota-Maccari system

Volume: 4 Number: 3 September 30, 2016
  • M. M. El-borai *
  • H. M. El-owaidy
  • Hamdy M. Ahmed
  • A. H. Arnous
EN

Soliton solutions of Hirota equation and Hirota-Maccari system

Abstract

In this paper, the trial equation method is presented to seek the exact solutions of two nonlinear partial differential equations (NLPDEs), namely, the Hirota equation and the Hirota-Maccari system. The obtained solutions are solitary, topological, singular solitons and singular periodic waves. This method is powerful, effective and it can be extended to many NLPDEs.


Keywords

References

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  4. Mahmoud M. El-Borai, Exact solutions for some nonlinear fractional parabolic fractional partial differential equations, Journal of Applied Mathematics and Computation 206 (2008,) 141-153.
  5. Mahmoud M. El-Borai, Afaf A. Zaghrout and Amal L. Elshaer, Exact solutions for nonlinear partial differential equations by using the extended multiple Riccati equations expansion method, Inter. J. of Research and Reviews in Applied Sciences, 9(3) (2011), 370-381.
  6. E. M. E. Zayed and A.H. Arnous, DNA dynamics studied using the homogeneous balance method, Chinese Physics Letters, 29(8) (2012), 080203.
  7. R. Hirota, Direct method of finding exact solutions of nonlinear evolution equations, in: R. Bulloygh, P. Coudrey (Eds.), Bäcklund transformation, Springer, Berlin, (1980).
  8. M. L. Wang, X. Li, Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation. Chaos Solit. Fract., 24 (2005), 1257-1268.

Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

M. M. El-borai * This is me
Egypt

H. M. El-owaidy This is me
Egypt

Hamdy M. Ahmed This is me
Egypt

A. H. Arnous This is me
Egypt

Publication Date

September 30, 2016

Submission Date

February 17, 2016

Acceptance Date

March 14, 2016

Published in Issue

Year 2016 Volume: 4 Number: 3

APA
El-borai, M. M., El-owaidy, H. M., Ahmed, H. M., & Arnous, A. H. (2016). Soliton solutions of Hirota equation and Hirota-Maccari system. New Trends in Mathematical Sciences, 4(3), 231-238. https://izlik.org/JA99JG35HG
AMA
1.El-borai MM, El-owaidy HM, Ahmed HM, Arnous AH. Soliton solutions of Hirota equation and Hirota-Maccari system. New Trends in Mathematical Sciences. 2016;4(3):231-238. https://izlik.org/JA99JG35HG
Chicago
El-borai, M. M., H. M. El-owaidy, Hamdy M. Ahmed, and A. H. Arnous. 2016. “Soliton Solutions of Hirota Equation and Hirota-Maccari System”. New Trends in Mathematical Sciences 4 (3): 231-38. https://izlik.org/JA99JG35HG.
EndNote
El-borai MM, El-owaidy HM, Ahmed HM, Arnous AH (September 1, 2016) Soliton solutions of Hirota equation and Hirota-Maccari system. New Trends in Mathematical Sciences 4 3 231–238.
IEEE
[1]M. M. El-borai, H. M. El-owaidy, H. M. Ahmed, and A. H. Arnous, “Soliton solutions of Hirota equation and Hirota-Maccari system”, New Trends in Mathematical Sciences, vol. 4, no. 3, pp. 231–238, Sept. 2016, [Online]. Available: https://izlik.org/JA99JG35HG
ISNAD
El-borai, M. M. - El-owaidy, H. M. - Ahmed, Hamdy M. - Arnous, A. H. “Soliton Solutions of Hirota Equation and Hirota-Maccari System”. New Trends in Mathematical Sciences 4/3 (September 1, 2016): 231-238. https://izlik.org/JA99JG35HG.
JAMA
1.El-borai MM, El-owaidy HM, Ahmed HM, Arnous AH. Soliton solutions of Hirota equation and Hirota-Maccari system. New Trends in Mathematical Sciences. 2016;4:231–238.
MLA
El-borai, M. M., et al. “Soliton Solutions of Hirota Equation and Hirota-Maccari System”. New Trends in Mathematical Sciences, vol. 4, no. 3, Sept. 2016, pp. 231-8, https://izlik.org/JA99JG35HG.
Vancouver
1.M. M. El-borai, H. M. El-owaidy, Hamdy M. Ahmed, A. H. Arnous. Soliton solutions of Hirota equation and Hirota-Maccari system. New Trends in Mathematical Sciences [Internet]. 2016 Sep. 1;4(3):231-8. Available from: https://izlik.org/JA99JG35HG