Conservation laws and invariants of motion for nonlinear internal waves: part II |
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| Authors: | Samir Hamdi Brian Morse Bernard Halphen William Schiesser |
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| Institution: | (1) Solid Mechanics Laboratory (LMS), Ecole Polytechnique, 91128 Palaiseau Cedex, Paris, France;(2) Department of Civil and Water Engineering, Laval University, Quebec, QC, G1V 0A6, Canada;(3) Mathematics and Engineering, Lehigh University, Bethlehem, PA 18015, USA |
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| 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. |
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