Have a personal or library account? Click to login
Geometry of coupled dispersionless equations with Mannheim curves Cover
By: Kemal Eren  
Open Access
|Oct 2023

References

  1. R. Blum, A Remarkable Class of Mannheim Curves. Canadian Mathematical Bulletin 9 (1966), 223-228.
  2. H. Liu, F. Wang, Mannheim Partner Curves in 3-Space. Journey of Geometry 88 (2008), 120-126.
  3. K. Orbay, E. Kasap, On Mannheim Partner Curves in E3. International Journal of Physical Sciences 4(5) (2009), 261-264.
  4. M. A. Güngör, M. Tosun, A Study on Dual Mannheim Partner Curves. International Mathematical Forum 5(47) (2010), 2319-2330.
  5. W. J. Lee, H. J. Choi, H. D. Jin, Slant Dual Mannheim Partner Curves in the Dual Space. Int. J. Contemp. Math. Science 31 (2011), 1535-1544.
  6. H. B. Öztekin, M. Ergüt, Null Mannheim Curves in the Minkowski 3-Space. Turk. J. Math. 35 (2011), 107114.
  7. M. Akyiğit, A. Z. Azak, Admissible Mannheim Curves in Pseudo-Galilean Space. Afr. Diaspora J. Math. (N.S.) 2 (2010), 58-65.
  8. M. Akyiğit, S. Ersoy, I. Özgür, M. Tosun, Generalized Timelike Mannheim Curves in Minkowski Space-Time E41. Math. Probl. Eng. 2011 (2011), 1-19, Article ID 539378.
  9. S. Ersoy, M. Tosun, H. Matsuda, Generalized Mannheim Curves in Minkowski Space-Time E14. Hokkaido Math. J. 41(3) (2012), 441-461.
  10. S. Ersoy, M. Masal, M. Tosun, On Mannheim Partner Curves of AW (k) Type. Uzbek. Mat. Zh. 1 (2014), 97107.
  11. K. S. Chou, C. Z. Qu, Integrable Equations Arising from Motions of Plane Curves. Physica, D. 162 (2002), 9-33.
  12. R. Myrzakulov, L. Martina, T. A. Kozhamkulov, Kur. Myrzakul, Integrable Heisenberg Ferromagnets and Soliton Geometry of Curves and Surfaces. In book: Nonlinear Physics: Theory and Experiment. II, World Scientific, London, 248-253, 2003.
  13. A. Myrzakul, R. Myrzakulov, Integrable Geometric Flows of Interacting Curves/Surfaces, Multilayer Spin Systems and the Vector Nonlinear Schrodinger Equation. Int. J. Geom. Methods Mod. 13(1) (2016), 1550134.
  14. A. Myrzakul, R. Myrzakulov, Integrable Motion of two Interacting Curves, Spin Systems and the Manakov System. Int. J. Geom. Methods Mod. 14(07) (2017), 1750115.
  15. J. Langer, R. Perline, Curve Motion Inducing Modified Korteweg-de Vries Systems. Phys. Lett. A. 239 (1998), 36-40.
  16. G. L. Lamb, Solitons on Moving Space Curves. J. Math. Phys. 18 (1977), 1654-1661.
  17. H. Hasimoto, A Soliton on a Vortex Filament. J. Fluid Mech. 51 (1972), 477-485.
  18. K. Konno, H. Oono, New Coupled Dispersionless Equations. J. Phys. Soc. Jpn. 63 (1994), 377378.
  19. K. Konno, H. Kakuhata, Interaction Among Growing, Decaying and Stationary Solitons for Coupled and Stationary Solitons. J. Phys. Soc. Jpn. 64 (1995), 27072709.
  20. H. Kakuhata, K. Konno, A Generalization of Coupled Integrable, Dispersionless System. J. Phys. Soc. Jpn. 65 (1996), 340341.
  21. H. Kakuhata, K. Konno, Lagrangian, Hamiltonian and Conserved Quantities for Coupled Integrable Dispersionless Equations. J. Phys. Soc. Jpn. 65 (1996), 12.
  22. S. F. Shen, B. F. Feng, Y. Ohta, From the Real and Complex Coupled Dispersionless Equations to the Real and Complex Short Pulse Equations. Stud. Appl. Math. 136 (2016), 64-88.
  23. B. F. Feng, K. Maruno, Y. Ohta, Geometric Formulation and Multi-Dark Soliton Solution to the Defocusing Complex Short Pulse Equation. Stud. Appl. Math. 138 (2017), 343367.
  24. B. F. Feng, K. Maruno, Y. Ohta, Self-Adaptive Moving Mesh Schemes for Short Pulse Type Equations and Their Lax Pairs. Pac. J. Math. Ind. 6 (2014), 720.
  25. B. ONeill, Elementary Di erential Geometry. Revised 2nd edition, Academic Press, USA, 2006.
DOI: https://doi.org/10.2478/auom-2023-0034 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 111 - 123
Submitted on: Sep 19, 2022
Accepted on: Dec 22, 2022
Published on: Oct 21, 2023
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2023 Kemal Eren, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.