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Moving non-null curves according to Bishop frame in Minkowski 3-space

Nevin Gürbüz

Mathematics — Computer Department, Eskişehir Osmangazi University, Türkiye

https://doi.org/10.1142/S0219887815500528Cited by:18 (Source: Crossref)

Abstract

In this paper, we introduce three new transformations and establish connections between moving non-null curves and soliton equations according to Bishop frame in Minkowski 3-space. Later we find formulas for differentials of these three new transformations associated with the nonlinear heat system and repulsive type nonlinear Schrödinger equation.

Keywords:

AMSC: 53B30, 53B50

References

H. Hasimoto , J. Fluid Mech. 51 , 477 ( 1972 ) . Crossref, Web of Science, Google Scholar
G. L. Lamb , J. Math. Phys. 18 , 1654 ( 1977 ) . Crossref, Web of Science, Google Scholar
M. Lakshmanan , Phys. Lett. A 61 , 53 ( 1977 ) . Crossref, Web of Science, Google Scholar
V. E. Zakharov and L. A. Takhtajan , Theor. Math. Phys. 38 , 26 ( 1979 ) . Crossref, Web of Science, Google Scholar
R. Hirota , J. Phys. Soc. Japan 51 , 323 ( 1982 ) . Crossref, Google Scholar
J. Langer and R. Perline , Appl. Math. Lett. 3 , 61 ( 1990 ) . Crossref, Google Scholar
J. Langer and R. Perline , Fields Inst. Commun. 7 , 171 ( 1997 ) . Google Scholar
J. Langer and R. Perline , Fields Inst. Commun. 7 , 181 ( 1997 ) . Google Scholar
C. Rogers and K. Schief , Stud. Appl. Math. 101 , 267 ( 1998 ) . Crossref, Web of Science, Google Scholar
S. Murugesh and R. Balakrishnan , Phys. Lett. A 290 , 81 ( 2001 ) . Crossref, Web of Science, Google Scholar
G. Muniraja and M. Lakshmanan , Int. J. Geom. Meth. Mod. Phys. 7 , 1043 ( 2010 ) . Link, Web of Science, Google Scholar
W.-Z. Zhao et al. , Commun. Theor. Phys. 44 , 415 ( 2005 ) . Crossref, Web of Science, Google Scholar
Q. Ding , X. Liu and W. Wang , J. Phys. A: Math. Theor. 45 , 45,5201 ( 2012 ) . Crossref, Web of Science, Google Scholar
Q. Ding and J. İnoguchi , Chaos, Solitons Fractals 21 , 669 ( 2004 ) . Crossref, Web of Science, Google Scholar
B. O'Neill , Semi-Riemannian Geometry with Applications to Relativity ( Academic Press , 1983 ) . Google Scholar
R. L. Bishop , Amer. Math. Monthly 82 , 246 ( 1975 ) . Crossref, Web of Science, Google Scholar
B. Bükcü and M. K. Karaçan , Commun. Fac. Sci. Univ. Ank. Sér. 57 , 13 ( 2008 ) . Crossref, Google Scholar
M. Özdemir and A. A. Ergin , Missouri J. Math. Sci. 20 , 127 ( 2008 ) . Crossref, Google Scholar