Advertisement

Group Classification of a Generalized Coupled Hyperbolic Lane–Emden System

  • Tshepo E. Mogorosi
  • Ben MuatjetjejaEmail author
Research Paper
  • 53 Downloads

Abstract

The aim of this work is to carry out a complete group classification of a generalized coupled hyperbolic Lane–Emden system. It is shown that the underling system admits six-dimensional equivalence Lie algebra. We further show that the principle Lie algebra which is one-dimensional extends in several cases. We also carry out Lie reductions for some cases.

Keywords

Group classification Generalized hyperbolic Lane–Emden system Lie point symmetries Symmetry reductions 

Mathematics Subject Classification

35J05 35G51 

Notes

Acknowledgements

T. E. Mogorosi thanks SANHARP for financial support. B. Muatjetjeja thanks the Faculty Research Committee (FAST), North-West University, Mafikeng Campus, South Africa, for its support.

References

  1. Bluman GW, Kumei S (1989) Symmetries and Differential Equations. Springer, New YorkCrossRefzbMATHGoogle Scholar
  2. Bozhkov Y, Freire IL (2012) Symmetry analysis of the bidimensional Lane–Emden systems. J Math Anal Appl 388:1279–1284MathSciNetCrossRefzbMATHGoogle Scholar
  3. Bozhkov Y, Martins ACG (2004) Lie point symmetries of the Lane–Emden systems. J Math Anal Appl 294:334–344MathSciNetCrossRefzbMATHGoogle Scholar
  4. Bozhkov Y, Mitidieri E (2007) Lie symmetries and criticality of semilinear differential systems, SIGMA, 3, paper 053Google Scholar
  5. Magalakwe G, Muatjetjeja B, Khalique CM (2015) Generalized double sinh- Gordon equation: symmetry reductions, exact solutions and conservation laws, Iran. J Sci Technol A 39:289–296MathSciNetzbMATHGoogle Scholar
  6. Mogorosi TE, Freire IL, Muatjetjeja B, Khalique CM (2017) Group analysis of a hyperbolic Lane–Emden system. Appl Math Comp 292:156–164MathSciNetCrossRefGoogle Scholar
  7. Molati M, Khalique CM (2012) Lie group classification of a generalized Lane-Emden type system in two dimensions. J Appl Math.  https://doi.org/10.1155/2012/405978 MathSciNetzbMATHGoogle Scholar
  8. Muatjetjeja B, Khalique CM (2010) Lagrangian approach to a generalized coupled Lane–Emden system: symmetries and first integrals. Nonlin Sci Numer Simul 15:1166–1171MathSciNetCrossRefzbMATHGoogle Scholar
  9. Muatjetjeja B, Khalique CM (2013) Conservation laws for a generalized coupled bidimensional Lane–Emden system. Commun Nonlin Sci Num Simul 18:851–857MathSciNetCrossRefzbMATHGoogle Scholar
  10. Muatjetjeja B, Khalique CM (2015) Symmetry analysis and conservation laws for a coupled (2+1)-dimensional hyperbolic system. Commun Nonlin Sci Numer Simul 22:1252–1262MathSciNetCrossRefzbMATHGoogle Scholar
  11. Muatjetjeja B, Khalique CM, Mahomed FM (2012) Group classification of a generalized Lane–Emden system. J Appl Math.  https://doi.org/10.1155/2013/305032 zbMATHGoogle Scholar
  12. Nouh MI, Abel-Salam Emad A-B (2017) Approximate solution to the fractional Lane–Emden type equations. Iran J Sci Technol A.  https://doi.org/10.1007/s40995-017-0246-5 Google Scholar
  13. Ovsiannikov LV (1982) Group Analysis of Differential Equations. Academic Press, New YorkzbMATHGoogle Scholar
  14. Serrin J, Zou H (1996) Non-existence of positive solutions of Lane–Eden systems. Differ Integral Equ 9:635–653zbMATHGoogle Scholar

Copyright information

© Shiraz University 2018

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNorth-West UniversityMmabathoRepublic of South Africa

Personalised recommendations