BibTex RIS Cite

Harry-Dym Hierarchy: Hereditary Operator and Ablowitz-Ramani-Segur Conjecture

Year 2015, Volume: 36 Issue: 3, 2206 - 2215, 13.05.2015

S.m. Hoseını , H. Sadeghı S. Eskandar

Abstract

Abstract. Using Lax representation, hereditary operator related to the Harry-Dym ( HD ) hierarchy is constructed. Also Lie analysis and Lax pair are used to drive the conserved quantities for the HD hierarchy. Lie symmetry method is also applied to study Painlev´e test for the family of HD hierarchy. It is found that for this family the Painlev´e property can be at most sufficient for integrability, but not necessary. This fact has been proved earlier for just first member of this family. 

Keywords

Lie analysis conservation laws hereditary operator Painlev´e property ARS conjecture

References

  • Vosconcelos G L and Koclanoff L P (1991) Phys. Rev. A 44 6490.
  • Hereman W, Banerjee P P and Chatterjee M R (1989) J. Phys. A: Math General 22 241.
  • Ablowitz M J and Segur H (1977) Phys. Rev. Lett 35 1103.
  • Tabor (1989) Chaos and Integrability in Nonlinear Dynamics: An Introduction New York: Whiley

Year 2015, Volume: 36 Issue: 3, 2206 - 2215, 13.05.2015

S.m. Hoseını , H. Sadeghı S. Eskandar

Abstract

References

  • Vosconcelos G L and Koclanoff L P (1991) Phys. Rev. A 44 6490.
  • Hereman W, Banerjee P P and Chatterjee M R (1989) J. Phys. A: Math General 22 241.
  • Ablowitz M J and Segur H (1977) Phys. Rev. Lett 35 1103.
  • Tabor (1989) Chaos and Integrability in Nonlinear Dynamics: An Introduction New York: Whiley
There are 4 citations in total.

Details

Journal Section Special
Authors

S.m. Hoseını

H. Sadeghı This is me

S. Eskandar This is me

Publication Date May 13, 2015
Published in Issue Year 2015 Volume: 36 Issue: 3

Cite

APA Hoseını, S., Sadeghı, H., & Eskandar, S. (2015). Harry-Dym Hierarchy: Hereditary Operator and Ablowitz-Ramani-Segur Conjecture. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, 36(3), 2206-2215.
AMA Hoseını S, Sadeghı H, Eskandar S. Harry-Dym Hierarchy: Hereditary Operator and Ablowitz-Ramani-Segur Conjecture. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. May 2015;36(3):2206-2215.
Chicago Hoseını, S.m., H. Sadeghı, and S. Eskandar. “Harry-Dym Hierarchy: Hereditary Operator and Ablowitz-Ramani-Segur Conjecture”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36, no. 3 (May 2015): 2206-15.
EndNote Hoseını S, Sadeghı H, Eskandar S (May 1, 2015) Harry-Dym Hierarchy: Hereditary Operator and Ablowitz-Ramani-Segur Conjecture. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36 3 2206–2215.
IEEE S. Hoseını, H. Sadeghı, and S. Eskandar, “Harry-Dym Hierarchy: Hereditary Operator and Ablowitz-Ramani-Segur Conjecture”, Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 36, no. 3, pp. 2206–2215, 2015.
ISNAD Hoseını, S.m. et al. “Harry-Dym Hierarchy: Hereditary Operator and Ablowitz-Ramani-Segur Conjecture”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi 36/3 (May 2015), 2206-2215.
JAMA Hoseını S, Sadeghı H, Eskandar S. Harry-Dym Hierarchy: Hereditary Operator and Ablowitz-Ramani-Segur Conjecture. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2015;36:2206–2215.
MLA Hoseını, S.m. et al. “Harry-Dym Hierarchy: Hereditary Operator and Ablowitz-Ramani-Segur Conjecture”. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi, vol. 36, no. 3, 2015, pp. 2206-15.
Vancouver Hoseını S, Sadeghı H, Eskandar S. Harry-Dym Hierarchy: Hereditary Operator and Ablowitz-Ramani-Segur Conjecture. Cumhuriyet Üniversitesi Fen Edebiyat Fakültesi Fen Bilimleri Dergisi. 2015;36(3):2206-15.