Simple two-layer dispersive models in the Hamiltonian reduction formalism

Abstract A Hamiltonian reduction approach is defined, studied, and finally used to derive asymptotic models of internal wave propagation in density stratified fluids two-dimensional domains. Beginning with the general formalism Benjamin (1986 J. Fluid Mech. 165 445–74) for an ideal, stably Euler fluid, corresponding structure systematically reduced setup two homogeneous under gravity, separated by interface confined between infinite horizontal plates. long-wave, small-amplitude asymptotics then obtain a simplified model that encapsulates most known properties dynamics such systems, as bidirectional maximal amplitude travelling waves form fronts. Further reductions, particular devising extension Dirac’s theory constraints, lead completely integrable evolution equations previously considered literature limiting forms fluids. To assess performance models, special solutions are studied compared those parent