THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

ON BACKLUND TRANSFORMATIONS OF SURFACES BY EXTENDED HARRY-DYM FLOW

ABSTRACT
The present paper deals with the introduction of Bäcklund transformations by Extended Harry-Dym Flow and with the aid of the extended version of the Riccati mapping method is obtained new solutions. Then, we give the Bäcklund transformation of the Schrödinger flow and obtain its the Bonnet surface. In finally, results obtained with the mathematical model are evaluated by applying to Mathematica.
KEYWORDS
PAPER SUBMITTED: 2019-02-20
PAPER REVISED: 2019-06-15
PAPER ACCEPTED: 2019-07-05
PUBLISHED ONLINE: 2019-09-15
DOI REFERENCE: https://doi.org/10.2298/TSCI190220342S
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2019, VOLUME 23, ISSUE Supplement 6, PAGES [S1823 - S1831]
REFERENCES
  1. Bäcklund, A. V.. Concerning surfaces with constant negative curvature, New Era, 1905.
  2. Do Carmo, M. P., Differential Geometry of Curves and Surfaces: Revised and Updated Second Edition. Courier Dover Publications, 2016.
  3. Goulart, C., Tenenblat, K., On Bäcklund and Ribaucour transformations for surfaces with constant negative curvature, Geometriae Dedicata, 181(1) (2016), pp. 83-102.
  4. Gökmen, Ö., Tosun, M., Özkald Karakus, S., A note on inextensible flows of curves in En, Int. Electron. J. Geom, 6(2) (2013), pp. 118-124.
  5. Ijaz, N., Bhatti, M. M., and Zeeshan A., Heat Transfer Analysis in MHD Flow of Solid Particles in Non-Newtonian Ree-Eyring Fluid due to Peristaltic Wave in A Channel, Thermal science, online first (doi. org/10.2298/TSCI170220155I).
  6. Griffiths, G. W. Bäcklund Transformation, www.researchgate.net/publication/ 269408982_Backlund_Transformation.
  7. Kwon, D. Y., & Park, F. C., Evolution of inelastic plane curves, Applied Mathematics Letters, 12(6) (1999), pp. 115-120.
  8. Kwon, D., Park, F. C., Chi, D. P., Inextensible flows of curves and developable surfaces, Applied Mathematics Letters, 18(10) (2005), pp. 1156-1162.
  9. Körpınar, T., & Turhan, E., Time Evolution Equations for Surfaces Generated via Binormal Spherical Image in Terms of Inextensible Flows in E3, Journal of Dynamical Systems and Geometric Theories, 12(2) (2014), pp. 145-157.
  10. Körpınar, T., & Turhan, E., New Approach for binormal spherical image in terms of inextensible flow in E3, Prespacetime Journal, 4(4) (2013).
  11. Körpınar, T., Demirkol, R.C., Asil, V., A Geometric Approach to the Harmonicity of the Unit Frenet-Serret Vector Fields in a Minkowski Space E 3 1, Journal of Advanced Physics, 7.3 (2018), pp. 359-365.
  12. Körpınar, T., Demirkol, R.C., Minimizing energy of the dynamical force fields via parallel vectors in the 3D space, Journal of Coupled Systems and Multiscale Dynamics, 6.3 (2018), pp. 184-190.
  13. Körpınar, T., A New Version of Fermi Walker Derivative with Constant Energy for Normal Image of Slant Helix in the Lie Groups, Differential Equations and Dynamical Systems, (2018), pp. 1-9.
  14. Körpinar, T., On velocity magnetic curves in terms of inextensible flows in space, Journal of Advanced Physics, 7.2 (2018), pp. 257-260.
  15. Korpinar, Z., On Numerical Solutions For The Caputo-Fabrızıo Fractional Heat-Like Equation, Thermal Science, (2018).
  16. Korpinar, Z., Inc. M., On RPS Algorithm of Fractional (1+ 1)-Dimensional Biswas-Milovic Equation, Journal of Advanced Physics, 7.1 (2018), pp. 92-97.
  17. Korpinar, Z., Inc. M., Numerical simulations for fractional variation of (1+ 1)-dimensional Biswas-Milovic equation, Optik, 166 (2018), pp. 77-85.
  18. Körpinar, Z., Tuz, M., and Körpınar, T., New Electromagnetic Fluids Inextensible Flows of Spacelike Particles and some Wave Solutions in Minkowski Space-time, International Journal of Theoretical Physics, 55.1 (2016), pp. 8-16.
  19. Körpınar, T., Demirkol, R.C., Gravitational magnetic curves on 3D Riemannian manifolds, International Journal of Geometric Methods in Modern Physics. 15 (2018), 1850184.
  20. Körpınar, T., Demirkol, R.C., Frictional magnetic curves in 3D Riemannian manifolds, International Journal of Geometric Methods in Modern Physics. 15 (2018), 1850020.
  21. Körpınar, T., Demirkol, R.C., Energy on a timelike particle in dynamical and electrodynamical force fields in De-Sitter space, Revista Mexicana de Fisica. 63 (2017), pp. 560-568.
  22. Körpınar, T., Demirkol, R.C., Asil, V., The motion of a relativistic charged particle in a homogeneous electromagnetic field in De-Sitter space, Revista Mexicana de Fisica. 64 (2018), pp. 176-180.
  23. Körpınar, T., Demirkol, R.C., On the uniform motion of a relativistic charged particle in a homogeneous electromagnetic field in Minkowski space E24, Math Meth Appl Sci, 42 (2019), pp. 3069-3087.
  24. Kwon, D., Park, F. C., & Chi, D. P., Inextensible flows of curves and developable surfaces, Applied Mathematics Letters, 18(10) (2005), pp. 1156-1162.
  25. Palmer, B., Bäcklund transformations for surfaces in Minkowski space, Journal of Mathematical Physics, 31(12) (1990), pp. 2872-2875.
  26. Schief, W. K., Isothermic surfaces in spaces of arbitrary dimension: integrability, discretization, and Bäcklund transformations---a discrete Calapso equation, Studies in Applied Mathematics, 106(1) (2001), pp. 85-137.
  27. Schief, W.K., Rogers, C., Binormal motion of curves of constant curvature and torsion. Generation of soliton surfaces, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci., 455 (1999), pp. 3163--3188.
  28. Qu, C., Han, J., & Kang, J., Bäcklund Transformations for Integrable Geometric Curve Flows. Symmetry, 7(3) (2015), pp. 1376-1394.

© 2020 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence