Geometric phase for timelike spherical normal magnetic charged particles optical ferromagnetic model

References

• Lakshmanan M, Rajainisursekar S. Nonlinear dynamics: integrability chaos and patterns. New York: Springer-Verlag; 2003.
   Google Scholar
• Matveev B, Salle MA. Darboux transformations and solitons. Berlin: Springer; 1991.
   Google Scholar
• Ablowitz MJ, Clarkson PA. Solitons, nonlinear evolution equations and inverse scattering transform. Cambridge: Cambridge Univ Press; 1990.
   Google Scholar
• Wang M, Zhou Y, Li Z. Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics. Phys Lett A. 1996;216:67–75. doi: 10.1016/0375-9601(96)00283-6
   Web of Science ®Google Scholar
• Miura RM. Backlund tra..nsformations, the inverse scattering method. Solitons and their applications: proceedings of the NSF Research Workshop on Contact Transformations. Nashville, Tennessee: Springer; 1974.
   Google Scholar
• Liu S, Fu Z, Liu S, et al. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Physics Letters A. 2001;289:69–74. doi: 10.1016/S0375-9601(01)00580-1
   Web of Science ®Google Scholar
• Conte R, Musette M. Link between solitary waves and projective Riccati equations. J Phys A: Math General. 1992;25(21):5609–5623. doi: 10.1088/0305-4470/25/21/019
   Google Scholar
• Hirota R. Direct methods in soliton theory, solitons. Berlin: Springer; 1980.
   Google Scholar
• Cao F. Geometric curve evolution and image processing. Germany: Springer Science & Business Media; 2003.
   Google Scholar
• Balakrishnan R, Bishop RA, Dandoloff R. Geometric phase in the classical continuous antiferromagnetic Heisenberg spin chain. Phys Rev Lett. 1990;64(18):2107–2110. doi: 10.1103/PhysRevLett.64.2107
   PubMed Web of Science ®Google Scholar
• Ding WY, Wang YD. Schrödinger flow of maps into symplectic manifolds. Sci China Ser A: Math. 1998;41(7):746–755. doi: 10.1007/BF02901957
   Google Scholar
• Koiso N. The vortex filament equation and a semi-linear Schrodinger equation in a Hermitian symmetric space. Osaka J Math. 1997;34(1):199.
   Web of Science ®Google Scholar
• Chang NH, Shatah J, Uhlenbeck K. Schrodinger maps. Commun Pure Appl Math A. 2000;53(5):590. doi: 10.1002/(SICI)1097-0312(200005)53:5<590::AID-CPA2>3.0.CO;2-R
   Web of Science ®Google Scholar
• Nahmod A, Stefanov A, Uhlenbeck K. On Schrodinger maps. Commun Pure Appl Math A. 2003;56(1):114–151. doi: 10.1002/cpa.10054
   Web of Science ®Google Scholar
• Balakrishnan R, Bishop AR, Dandoloff R. Anholonomy of a moving space curve all applications to classical magnetic chains. Phys Rev B. 1993;47:3108–3117. doi: 10.1103/PhysRevB.47.3108
   Web of Science ®Google Scholar
• Balakrishnan R, Dandoloff R. The Schrödinger equation as a moving curve. Phys Lett A. 1999;260:62–67. doi: 10.1016/S0375-9601(99)00492-2
   Web of Science ®Google Scholar
• Berrry MV. Quantal phase factors accompanying adiabatic changes. Proc R Soc Lond A Math Phys Sci. 1984;392:45.
   Google Scholar
• Kwon DY, Park FC, Chi DP. Inextensible flows of curves and developable surfaces. Appl Math Lett. 2005;18:1156–1162. doi: 10.1016/j.aml.2005.02.004
   Web of Science ®Google Scholar
• Körpinar T, Demirkol RC. Magnetic motion of spherical frictional charged particles on the unit sphere. Revista Mexicana De Fisica. 2019;65(5):496. doi: 10.31349/RevMexFis.65.496
   Web of Science ®Google Scholar
• Körpınar T. On the Fermi-Walker derivative for inextensible flows. Zeitschrift Für Naturforschung A. 2015;70(7):477–482. doi: 10.1515/zna-2015-0044
   Google Scholar
• Körpınar T, Turhan E. A new version of inextensible flows of spacelike curves with timelike B2 in Minkowski space-Time E14. Differ Equ Dyn Syst. 2013;21(3):281–290. doi: 10.1007/s12591-012-0152-4
   Google Scholar
• Körpınar Z, Inc M. On the Biswas–Milovic model with power law nonlinearity. J Adv Phys. 2018;7(2):239–246. doi: 10.1166/jap.2018.1416
   Google Scholar
• Körpınar T. On inextensible flows of curves according to alternative moving frame. J Dyn Syst & Geometric Theor. 2017;15(1):15–27. doi: 10.1080/1726037X.2017.1323416
   Web of Science ®Google Scholar
• Chen G, Wang Q. Local fields in single-mode helical fibres. Opt Quantum Electron. 1995;27:1069–1074. doi: 10.1007/BF00292136
   Web of Science ®Google Scholar
• Fang XS, Lin ZQ. Field in single-mode helically-wound optical fibers. IEEE Trans Microwave Theory Tech MTT. 1985;33:1150–1154. doi: 10.1109/TMTT.1985.1133187
   Web of Science ®Google Scholar
• Körpinar T, Demirkol RC, Körpinar Z. Soliton propagation of electromagnetic field vectors of polarized light raytraveling along with coiled optical fiber on the unit 2-sphere S2. Revista Mexicana De Fisica. 2019;65(6):626. doi: 10.31349/RevMexFis.65.626
   Web of Science ®Google Scholar
• Körpinar T, Demirkol RC, Asil V. The motion of a relativistic charged particle in a homogeneous electromagnetic field in De-Sitter space. Revista Mexicana De Fisica. 2018;64:176. doi: 10.31349/RevMexFis.64.176
   Web of Science ®Google Scholar
• Körpınar T. On velocity magnetic curves in terms of inextensible flows in space. J Adv Phys. 2018;7(2):257–260. doi: 10.1166/jap.2018.1420
   Google Scholar
• Carmo MP. Differential geometry of curves and surfaces. New Jersey: Prentice-Hall; 1976.
   Google Scholar