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Conservation Laws for a Generalized Coupled Korteweg-de Vries System

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  • Daniel Mpho Nkwanazana
  • Ben Muatjetjeja
  • Chaudry Masood Khalique

Abstract

We construct conservation laws for a generalized coupled KdV system, which is a third-order system of nonlinear partial differential equations. We employ Noether's approach to derive the conservation laws. Since the system does not have a Lagrangian, we make use of the transformation , and convert the system to a fourth-order system in , . This new system has a Lagrangian, and so the Noether approach can now be used to obtain conservation laws. Finally, the conservation laws are expressed in the , variables, and they constitute the conservation laws for the third-order generalized coupled KdV system. Some local and infinitely many nonlocal conserved quantities are found.

Suggested Citation

  • Daniel Mpho Nkwanazana & Ben Muatjetjeja & Chaudry Masood Khalique, 2013. "Conservation Laws for a Generalized Coupled Korteweg-de Vries System," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-5, July.
    • Handle: RePEc:hin:jnlmpe:240797
    DOI: 10.1155/2013/240797
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    Cited by:

    1. Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Khalique, Chaudry Masood & Unlu, Canan, 2021. "Neuro-evolution computing for nonlinear multi-singular system of third order Emden–Fowler equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 799-812.

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