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Lagrangian Formulation, Conservation Laws, Travelling Wave Solutions: A Generalized Benney-Luke Equation

Author

Listed:
  • Sivenathi Oscar Mbusi

    (Departement of Mathematical Sciences, North-West University, Private Bag X 2046, Mmabatho 2735, South Africa)

  • Ben Muatjetjeja

    (Departement of Mathematical Sciences, North-West University, Private Bag X 2046, Mmabatho 2735, South Africa
    Department of Mathematics, Faculty of Science, University of Botswana, Private Bag 22, Gaborone, Botswana)

  • Abdullahi Rashid Adem

    (Department of Mathematical Sciences, University of South Africa, Pretoria 0003, South Africa)

Abstract

The aim of this paper is to find the Noether symmetries of a generalized Benney-Luke equation. Thereafter, we construct the associated conserved vectors. In addition, we search for exact solutions for the generalized Benney-Luke equation through the extended tanh method. A brief observation on equations arising from a Lagrangian density function with high order derivatives of the field variables, is also discussed.

Suggested Citation

  • Sivenathi Oscar Mbusi & Ben Muatjetjeja & Abdullahi Rashid Adem, 2021. "Lagrangian Formulation, Conservation Laws, Travelling Wave Solutions: A Generalized Benney-Luke Equation," Mathematics, MDPI, vol. 9(13), pages 1-6, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1480-:d:581195
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    References listed on IDEAS

    as
    1. Li, Bacui & Zhang, Yufeng, 2008. "Explicit and exact travelling wave solutions for Konopelchenko–Dubrovsky equation," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1202-1208.
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