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

Samir Hamdi (), Brian Morse, Bernard Halphen and William Schiesser

Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, 2011, vol. 57, issue 3, 609-616

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

Keywords: Generalized Gardner equation; Conservation laws; Invariants of motion; Internal waves; Solitary waves (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1007/s11069-011-9737-4

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