THERMAL SCIENCE
International Scientific Journal
ON EXACT SOLUTIONS FOR NEW COUPLED NONLINEAR MODELS GETTING EVOLUTION OF CURVES IN GALILEAN SPACE
ABSTRACT
In this work, the new coupled nonlinear partial differential equations (CNLPDEs) getting the time evolution of the curvatures of the evolving curve are derived in the Galilean space. Exact solutions for these new CNLPDEs are obtained. Finally, Lie symmetry analysis is performed on these new CNLPDEs and the algebra of Lie point symmetries of these new equations is found.
KEYWORDS
PAPER SUBMITTED: 2018-10-15
PAPER REVISED: 2018-11-20
PAPER ACCEPTED: 2019-01-17
PUBLISHED ONLINE: 2019-03-09
THERMAL SCIENCE YEAR
2019, VOLUME
23, ISSUE
Supplement 1, PAGES [S227 - S233]
- Hasimoto, H., A Soliton on a Vortex Filament, J. Fluid Mech.,51 (1972), 3, pp. 477-485
- Lamb, G. L., Solitons on Moving Space Curves, J. Math. Phys.,18 (1977), 8, pp. 1654-1661
- Abdel-All, N. H., et al., Evolution of Curves via the Velocities of the Moving Frame, J. Math. Comput. Sci.,2 (2012), 5, pp. 1170-1185
- Abdel-All, N. H., et al., Geometry of Evolving Plane Curves Problem via Lie Group Analysis, Stud.Math. Sci.,2 (2011), 1, pp. 51-62
- Ogrenmis, A. O. et al., Inextensible Curves in the Galilean Space, Int. J. Phys. Sci., 5 (2010), 9, pp. 1424-1427
- Yuzbasi, Z.K., et al., Inelastic Flows of Curves on Light Like Surfaces, Mathematics, 6 (2018), 11, pp. 224
- Yuzbasi, Z. K., et al., A Note on Inextensible Flows of Partially & Pseudo Null Curves in E_1^4, Pre-spacetime J., 7 (2016), 5, pp. 818-827
- Khater, A. H., et al., Nonlinear Dispersive Instabilities in Kelvin-Helmhooltz Magnetohynamic Flows, Phys. Scrip., 67 (2003), 4, pp. 340-349
- Khater, A. H., et al., General Soliton Solutions of an N-Dimensional Nonlinear Schroudinger Equation, IL Nuovo Cimento (B),115 (2000), 11, pp. 1303-1312
- Biswas, A., et al., Solitons in Optical Materials by Functional Variable Method and First Integral Ap-proach, Frequenz,68 (2014), 11-12, pp. 525-530
- Mirzazadeh, M., et al., Optical Solitons in Nonlinear Directional Couplers by Sine-Cosine Function Method and Bernoulli’s Equation Approach, Nonl. Dyn.,81 (2015), 4, pp. 1933-1949
- Yildirim, Y., et al., Lie Symmetry Analysis and Exact Solutions to N-Coupled Nonlinear Schrödinger’s Equations with Kerr and Parabolic Law Nonlinearities, Rom. J. of Phys.,63 (2018), 103, pp. 1-12
- Bansal, A., et al., Optical Soliton Perturbation with Radhaskrishnan-Kundu-Lakshmanan Equation by Lie Group Analysis, Optik, 163 (2017), Jun, pp. 137-141
- Biswas, A., et al., Conservation Laws for Gerdjikov-Ivanov Equation in Nonlinear Fiber Optics and PCF, Optik, 148 (2017), Nov., pp. 209-214
- Bansal, A., et al., Optical Solitons and Group Invariant Solutions to Lakshmanan–Porsezian–Daniel Mod-el in Optical Fibers and PCF, Optik,160 (2018), May, pp. 86-91
- Morris, R., et al., On Symmetries, Reductions, Conservation Laws and Conserved Quantities of Optical Solitons with Inter-Modal Dispersion, Optik,124 (2013), 21, pp. 5116-5123
- Fakhar, K., et al., Symmetry Reductions and Conservation Laws of the Short Pulse Equation, Optik, 127(2016), 21, pp. 10201-10207
- Hashemi, M. S., et al., Lie Symmetry Analysis of Steady-State Fractional Reaction-Convection-Difusion Equation, Optik, 138 (2017), June, pp. 240-249
- Yuzbasi, Z. K., et al., Lie Symmetry Analysis and Exact Solutions of Tzitzeica Surpaces PDE in Galilean Space, J. Adv. Phys.,7 (2018), 1, pp. 88-91
- Pavkovic, B. J., et al., The Equiform Differential Geometry of Curves in the Galilean Space G3, Glasnik Math.,22 (2008), 42, pp. 449-457
- Lipschutz, M., Theory and Problems of Differential Geometry, Schaum’s Outline Series, McGraw-Hill, Ney York, USA, 1969
- Sahin, T., Intrinsic Equations for a Generalized Relaxed Elastic Line on an Oriented Surface in the Gali-lean Space, Acta Math. Sci.,33 (2013), 3, pp. 701-711
- Baldwin, D., et al., Symbolic Computation of Exact Solutions Expressible in Hyperbolic and Eliptic Functions for Nonlinear PDEs, J. Symb. Comput.,37 (2004), 6, pp. 669-705
- Olver, P. J., Applications of Lie Groups to Differential Equations, 2nd ed., G.T.M, Springer-Verlag. New York, USA, 1993
- Bluman, G., et al.,Symmetry and Integration Methods for Differential Equations, Springer Science & Business Media, New York, USA, 2008