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Application of the Composite Variational Principle to Shallow Water Equations

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Abstract

In this study, we derive new local conservation laws of the one-layer shallow water equations in the plane flow which are belong to the family of evolution type equations by the composite variational principle of view in the development of the study (N.H. Ibragimov, A new conservation theorem. J. Math. Anal. Appl. 333:311–328, 2007).

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Acknowledgements

This work is part of the PhD thesis of the first author Emrullah Yasar.

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Authors and Affiliations

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

    Emrullah Yasar

  2. Faculty of Civil Engineering, Division of Mechanics, Istanbul Technical University, 34469, Istanbul, Turkey

    Teoman Ozer

Authors
  1. Emrullah Yasar
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  2. Teoman Ozer
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Corresponding author

Correspondence to Emrullah Yasar .

Editor information

Editors and Affiliations

  1. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    J.A. Tenreiro Machado

  2. Dept. of Mech. & Industr. Engineering, Southern Illinois Univ. Edwardsville, Edwardsville, 62026-1805, Illinois, USA

    Albert C.J. Luo

  3. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    Ramiro S. Barbosa

  4. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    Manuel F. Silva

  5. Institute of Engineering, Dept. Electrotechnical Engineering, Polytechnic Institute of Porto, Rua Dr. Antonio Bernardino de Almeida 431, Porto, 4200-072, Portugal

    Lino B. Figueiredo

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Yasar, E., Ozer, T. (2011). Application of the Composite Variational Principle to Shallow Water Equations. In: Machado, J., Luo, A., Barbosa, R., Silva, M., Figueiredo, L. (eds) Nonlinear Science and Complexity. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9884-9_8

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  • DOI: https://doi.org/10.1007/978-90-481-9884-9_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-9883-2

  • Online ISBN: 978-90-481-9884-9

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