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Variational principles and conservation laws to the Burridge–Knopoff equation

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Abstract

We generate conservation laws for the Burridge–Knopoff equation which model nonlinear dynamics of earthquake faults by a new conservation theorem proposed recently by Ibragimov. One can employ this new general theorem for every differential equation (or systems) and derive new local and nonlocal conservation laws. Nonlocal conservation laws comprise nonlocal variables defined by the adjoint equations to the Burridge–Knopoff equation.

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References

  1. Ibragimov, N.H., Kara, A.H., Mahomed, F.M.: Lie-Backlund and Noether symmetries with applications. Nonlinear Dyn. 15(2), 115–136 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  2. Kara, A.H., Khalique, C.M.: Conservation laws and associated symmetries for some classes of soil water motion equations. Int. J. Non-Linear Mech. 36(7), 1041–1045 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  3. Ibragimov, N.H.: A new conservation theorem. J. Math. Anal. Appl. 333(1), 311–328 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ibragimov, N.H., Kolsrud, T.: Lagrangian approach to evolution equations: symmetries and conservation laws. Nonlinear Dyn. 36(1), 29–40 (2004)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  6. Anco, S.C., Bluman, G.: Direct construction method for conservation laws of partial differential equations, part I: examples of conservation laws classifications. Eur. J. Appl. Math. 13, 547 (2001)

    Google Scholar 

  7. Burridge, R., Knopoff, L.: Model and theoretical seismicity. Bull. Seism. Soc. Am. 57, 341–371 (1967)

    Google Scholar 

  8. He, J.H.: A variational approach to the Burridge–Knopoff equation. Appl. Math. Comput. 144, 1–2 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. Ibragimov, N.H.: Elementary Lie Group Analysis and Ordinary Differential Equations. Wiley, Chichester (1999)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Science, Uludag University, Görükle, 16059, Bursa, Turkey

    Emrullah Yaşar

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  1. Emrullah Yaşar
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Correspondence to Emrullah Yaşar.

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Yaşar, E. Variational principles and conservation laws to the Burridge–Knopoff equation. Nonlinear Dyn 54, 307–312 (2008). https://doi.org/10.1007/s11071-008-9330-x

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  • DOI: https://doi.org/10.1007/s11071-008-9330-x

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