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Analysis of Generalized BBM Equations: Symmetry Groups and Conservation Laws

In: Current Trends in Mathematical Analysis and Its Interdisciplinary Applications

Author

Listed:
  • M. S. Bruzón

    (Universidad de Cádiz, Departamento de Matemáticas)

  • T. M. Garrido

    (Universidad de Cádiz, Departamento de Matemáticas)

  • R. de la Rosa

    (Universidad de Cádiz, Departamento de Matemáticas)

Abstract

In this work we study a generalized BBM equation from the point of view of the theory of symmetry reductions in partial differential equations. We obtain the Lie symmetries, then we use the transformation groups to reduce the equations into ordinary differential equations. Physical interpretation of these reductions and some exact solutions are also provided. Local conservation laws are continuity equations that provide conserved quantities of physical importance for all solutions of a particular equation. In addition, the existence of an infinite hierarchy of local conservation laws of a partial differential equation is a strong indicator of its integrability. For any particular partial differential equation, a complete classification of all local low-order conservation laws can be derived by using the multiplier method.

Suggested Citation

  • M. S. Bruzón & T. M. Garrido & R. de la Rosa, 2019. "Analysis of Generalized BBM Equations: Symmetry Groups and Conservation Laws," Springer Books, in: Hemen Dutta & Ljubiša D. R. Kočinac & Hari M. Srivastava (ed.), Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, chapter 0, pages 197-228, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-15242-0_7
    DOI: 10.1007/978-3-030-15242-0_7
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