International Journal of Theoretical Physics

, Volume 47, Issue 11, pp 3075–3081 | Cite as

Conservation Laws and Associated Noether Type Vector Fields via Partial Lagrangians and Noether’s Theorem for the Liang Equation

  • D. N. Khan Marwat
  • A. H. Kara
  • T. Hayat


We show how one can construct conservation laws of the Liang equation which is not variational but may be regarded as Euler-Lagrange in part. This first requires the determination of the Noether-type symmetries associated with the partial Lagrangian. The final construction of the conservation laws resort to a formula equivalent to Noether’s theorem. A variety of subclasses are given and, for each, a large number of conserved flows are found—the method is usable for any general choice of the variable speed of sound.


Inhomogeneous wave and Liang equation Noether-type symmetries Partial Lagrangians Conservation laws 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsCOMSATS Institute of Information TechnologyIslamabadPakistan
  2. 2.School of MathematicsUniversity of the WitwatersrandWitsSouth Africa
  3. 3.Department of MathematicsQuaid-i-Azam UniversityIslamabadPakistan

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