THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

LIE SYMMETRY GROUP OF (2+1)-DIMENSIONAL JAULENT-MIODEK EQUATION

ABSTRACT
In this paper, we consider a system of (2+1)-dimensional non-linear model by using auxiliary equation method and Clarkson-Kruskal direct method which is very important in fluid and physics. We construct some new exact solutions of (2+1)-dimensional non-linear models with the aid of symbolic computation which can illustrate some actions in fluid in the future.
KEYWORDS
PAPER SUBMITTED: 2014-03-10
PAPER REVISED: 2014-04-30
PAPER ACCEPTED: 2014-07-12
PUBLISHED ONLINE: 2015-01-04
DOI REFERENCE: https://doi.org/10.2298/TSCI1405547M
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2014, VOLUME 18, ISSUE 5, PAGES [1547 - 1552]
REFERENCES
  1. Parkes, E. J., Duffy, B. R., An Automated Tanh-Function Method for Finding Solitary Wave Solutions to Non-Linear Evolution Equations, Computer Physics Communications, 98 (1996), 2, pp. 288-300
  2. Gao, Y. T., Tian, B., Generalized Hyperbolic-Function Method with Computerized Symbolic Computation to Construct the Solitonic Solutions to Non-linear Equations of Mathematical Physics, Computer Physics Communications, 133 (2001), 2, pp. 158-164
  3. Wang, M. L., et al., Application of a Homogeneous Balance Method to Exact Solutions of Non-linear Equations in Mathematical Physics, Physics Letters A, 216 (1996), 1, pp. 67-75
  4. Liu, S., et al., Jacobi Elliptic Function Expansion Method and Periodic Wave Solutions of Non-linear Wave Equations, Physics Letters A, 289 (2001), 1, pp. 69-74
  5. He, J.-H., Wu, X.-H., Exp-Function Method for Non-linear Wave Equations, Chaos, Solitons & Fractals, 30 (2006), 3, pp. 700-708
  6. Sirendaoreji, New Exact Travelling Wave Solutions for the Kawahara and Modified Kawahara Equations, Chaos, Solitons & Fractals, 19 (2004), 1, pp. 147-150
  7. Ma, H. C., Generating Lie Point Symmetry Groups of (2+1)-Dimensional Broer-Kaup Equation via a Simple Direct Method, Communications in Theoretical Physics, 43 (2005), 6, pp. 1047-1052
  8. Ma, H. C., et al., Lie Symmetry Groups of (2+1)-Dimensional BKP Equation and Its New Solutions, Communications in Theoretical Physics, 50 (2008), 3, pp. 685-688
  9. Sirendaoreji, Sun, J., Auxiliary Equation Method for Solving Non-linear Partial Differential Equations, Physics Letters A, 309 (2003), 5, pp. 387-396
  10. Ma, H. C., et al., The Auxiliary Equation Method for Solving the Zakharov-Kuznetsov (ZK) Equation, Computers & Mathematics with Applications, 58 (2009), 11, pp. 2523-2527
  11. Geng, X. G., et al., Quasi-Periodic Solutions for Some (2+1)-Dimensional Integrable Models Generated by the Jaulent-Miodek Hierarchy, Journal of Physics A: Mathematical and General, 34 (2001), 5, pp. 989-1004
  12. Jaulent, M., Miodek, I., Non-linear Evolution Equations Associated with Energy-Dependent Schrodinger Potentials, Letters in Mathematical Physics, 1 (1976), 3, pp. 243-250
  13. Wu, J., N-Soliton Solution, Generalized Double Wronskian Determinant Solution and Rational Solution for a (2+1)-Dimensional Non-linear Evolution Equation, Physics Letters A, 373 (2008), 1, pp. 83-88
  14. Liu, H., Yan, F., The Bifurcation and Exact Travelling Wave Solutions for (2+1)-Dimensional Nonlinear Models Generated by the Jaulent-Miodek Hierarchy, International Journal of Non-linear Science, 11 (2011), 1, pp. 200-205
  15. Wazwaz, A. M., Multiple Kink Solutions and Multiple Singular Kink Solutions for (2+1)-Dimensional Non-linear Models Generated by the Jaulent-Miodek Hierarchy, Physics Letters A, 373 (2009), 21, pp. 1844-1846
  16. Lie, S., Lectures on Differential Equations with Known Infinitesimal Transformations, Teubner, Leipzig, Germany, 1891
  17. Clarkson, P. A., Kruskal, M. D., New Similarity Reductions of the Boussinesq Equation, Journal of Mathematical Physics, 30 (1989), 10, pp. 2201-2213
  18. Lou, S., Ma, H. C., Non-Lie Symmetry Groups of (2+1)-Dimensional Non-linear Systems Obtained From a Simple Direct Method, Journal of Physics A: Mathematical and General, 38 (2005), 7, pp. L129-L137
  19. Ma, H. C., et al., Symmetry Transformation and New Exact Multiple Kink and Singular Kink Solutions for (2+1)-Dimensional Non-linear Models Generated by the Jaulent-Miodek Hierarchy, Communications in Theoretical Physics, 59 (2013), 2, pp. 141-145

© 2019 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