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Conservation laws and invariants of motion for nonlinear internal waves: part II

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Listed:
  • Samir Hamdi
  • Brian Morse
  • Bernard Halphen
  • William Schiesser

Abstract

In this paper, we derive three conservation laws and three invariants of motion for the generalized Gardner equation. These conserved quantities for internal waves are the momentum, energy, and Hamiltonian. The approach used for the derivation of these conservation laws and their associated invariants of motion is direct and does not involve the use of variational principles. It can be easily applied for finding similar invariants of motion for other general types of KdV, Gardner, and Boussinesq equations. The stability and conservation properties of discrete schemes for the simulations of internal waves propagation can be assessed and monitored using the analytical expressions of the constants of motion that are derived in this work. Copyright Springer Science+Business Media B.V. 2011

Suggested Citation

  • Samir Hamdi & Brian Morse & Bernard Halphen & William Schiesser, 2011. "Conservation laws and invariants of motion for nonlinear internal waves: part II," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 57(3), pages 609-616, June.
    • Handle: RePEc:spr:nathaz:v:57:y:2011:i:3:p:609-616
    DOI: 10.1007/s11069-011-9737-4
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    1. Samir Hamdi & Brian Morse & Bernard Halphen & William Schiesser, 2011. "Analytical solutions of long nonlinear internal waves: Part I," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 57(3), pages 597-607, June.
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