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On double reductions from symmetries and conservation laws for a damped Boussinesq equation

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  • Gandarias, M.L.
  • Rosa, M.

Abstract

In this work, we study a Boussinesq equation with a strong damping term from the point of view of the Lie theory. We derive the classical Lie symmetries admitted by the equation as well as the reduced ordinary differential equations. Some nontrivial conservation laws are derived by using the multipliers method. Taking into account the relationship between symmetries and conservation laws and applying the double reduction method, we obtain a direct reduction of order of the ordinary differential equations and in particular a kink solution.

Suggested Citation

  • Gandarias, M.L. & Rosa, M., 2016. "On double reductions from symmetries and conservation laws for a damped Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 560-565.
    • Handle: RePEc:eee:chsofr:v:89:y:2016:i:c:p:560-565
    DOI: 10.1016/j.chaos.2016.03.030
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    References listed on IDEAS

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    1. M. L. Gandarias & M. S. Bruzón & M. Rosa, 2015. "Symmetries and Conservation Laws for Some Compacton Equation," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-6, August.
    2. Tracinà, R. & Bruzón, M.S. & Gandarias, M.L., 2016. "On the nonlinear self-adjointness of a class of fourth-order evolution equations," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 299-304.
    3. N. Mindu & D. P. Mason, 2014. "Derivation of Conservation Laws for the Magma Equation Using the Multiplier Method: Power Law and Exponential Law for Permeability and Viscosity," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-13, May.
    4. Khadijo Rashid Adem & Chaudry Masood Khalique, 2015. "Symmetry Analysis and Conservation Laws of a Generalized Two-Dimensional Nonlinear KP-MEW Equation," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-7, July.
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    Cited by:

    1. Yıldırım, Yakup & Yaşar, Emrullah, 2018. "A (2+1)-dimensional breaking soliton equation: Solutions and conservation laws," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 146-155.
    2. Juan Arturo Alvarez-Valdez & Guillermo Fernandez-Anaya, 2023. "Roadmap of the Multiplier Method for Partial Differential Equations," Mathematics, MDPI, vol. 11(22), pages 1-57, November.

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