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

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Abstract

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.

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References

  1. Anco, S.C., Bluman, G.W.: Direct construction method for conservation laws of partial differential equations. Part II: General treatment. Eur. J. Appl. Math. 9, 567–585 (2002)

    MathSciNet  Google Scholar 

  2. Carbonaro, P., Giambo, S.: Invariance properties and exact solutions of the Liang equation. Nuovo Cimento B 116(12), 1331–1352 (2001)

    ADS  MathSciNet  Google Scholar 

  3. Kara, A.H., Mahomed, F.M.: Relationship between symmetries and conservation laws. Int. J. Theor. Phys. 39, 23–40 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  4. Kara, A.H., Mahomed, F.M.: A basis of conservation laws for partial differential equations. J. Nonlin. Math. Phys. 9, 60–72 (2002)

    Article  MathSciNet  Google Scholar 

  5. Kara, A.H., Mahomed, F.M.: Noether-type symmetries and conservation laws via partial Lagrangians. Nonlinear Dyn. 45(3–4), 367–383 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  6. Landau, L., Lifchitz, E.: Mé canique des fluides. Mir, Moscow (1967)

    Google Scholar 

  7. Liang, E.P.T.: Astrophys. J., 361 (1977)

  8. Marwat, D.N.K., Kara, A.H., Mahomed, F.M.: Symmetries, conservation laws and multipliers via partial Lagrangians and Noether’s Theorem for classically non variational problems. Int. J. Theor. Phys. 46(12), 3022–3029 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  9. Noether, E.: Invariante Variationsprobleme. Nachr. Akad. Wiss., Gött. Math.-Phys. Kl. 2, 235–257 (1918). (English translation in Transp. Theory Stat. Phys. 1(3), 186–207 (1971))

    Google Scholar 

  10. Wolf, T.: A comparison of four approaches to the calculation of conservation laws. Eur. J. Appl. Math. 13, 129–152 (2002)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, COMSATS Institute of Information Technology, H-8, Islamabad, Pakistan

    D. N. Khan Marwat

  2. School of Mathematics, University of the Witwatersrand, Wits, 2050, South Africa

    A. H. Kara

  3. Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

    T. Hayat

Authors
  1. D. N. Khan Marwat
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  2. A. H. Kara
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  3. T. Hayat
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Correspondence to A. H. Kara.

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Marwat, D.N.K., Kara, A.H. & Hayat, T. Conservation Laws and Associated Noether Type Vector Fields via Partial Lagrangians and Noether’s Theorem for the Liang Equation. Int J Theor Phys 47, 3075–3081 (2008). https://doi.org/10.1007/s10773-008-9739-5

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  • DOI: https://doi.org/10.1007/s10773-008-9739-5

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