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Nonlinear Self-Adjointness for some Generalized KdV Equations

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Discontinuity and Complexity in Nonlinear Physical Systems

Part of the book series: Nonlinear Systems and Complexity ((NSCH,volume 6))

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Abstract

The new concepts of self-adjoint equations formulated in Gandarias (J Phys A: Math Theor 44:262001, 2011) and Ibragimov (J Phys A: Math Theor 44:432002, 2011) are applied to some classes of third order equations. Then, from Ibragimov’s theorem on conservation laws, conservation laws for two generalized equations of KdV type and a potential Burgers equation are established.

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Acknowledgements

The support of DGICYT project MTM2009-11875 and Junta de Andalucía group FQM-201 is gratefully acknowledged.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de Cádiz, 11510, Puerto Real, Cádiz, Spain

    M. L. Gandarias & M. Rosa

Authors
  1. M. L. Gandarias
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  2. M. Rosa
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Corresponding author

Correspondence to M. L. Gandarias .

Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, Polytechnic Institute of Porto Institute of Engineering, Porto, Portugal

    J. A. Tenreiro Machado

  2. Faculty of Art and Sciences, Mathematics and Computer Sciences, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

  3. Department of Mechanical Engineering, Southern Illinois University Edwardsville, Edwardsville, Illinois, USA

    Albert C J Luo

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Gandarias, M.L., Rosa, M. (2014). Nonlinear Self-Adjointness for some Generalized KdV Equations. In: Machado, J., Baleanu, D., Luo, A. (eds) Discontinuity and Complexity in Nonlinear Physical Systems. Nonlinear Systems and Complexity, vol 6. Springer, Cham. https://doi.org/10.1007/978-3-319-01411-1_1

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  • DOI: https://doi.org/10.1007/978-3-319-01411-1_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-01410-4

  • Online ISBN: 978-3-319-01411-1

  • eBook Packages: EngineeringEngineering (R0)

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