Nonlinear wave motion is studied in a symmetric, continuously stratified, smoothed three-layer fluid in the framework of the fully nonlinear Euler equations under the Boussinesq approximation. The weakly nonlinear limit is discussed in which the governing equations can be reduced to the fully integrable modified Korteweg-de Vries equation. For some choices of the layer thicknesses the cubic nonlinear term is positive and the modified Korteweg-de Vries equation has soliton and breather solutions. Using such a stratification, the Euler equations are solved numerically using a sign-variable, initial disturbance. Breathers were generated for several forms of the initial disturbance. The breathers have moderate amplitude and to a good approximation can be described by the modified Korteweg-de Vries equation. As far as we know this is the first presentation of a breather in numerical simulations using the full nonlinear Euler equations for a stratified fluid.

Abstract. The transformation of nonlinear long internal waves in a two-layer fluid is studied in the Boussinesq and rigid-lid approximation. Explicit analytic formulation of the evolution equation in terms of the Riemann invariants allows us to obtain analytical results characterizing strongly nonlinear wave steepening, including the spectral evolution. Effects manifesting the action of high nonlinear corrections of the model are highlighted. It is shown, in particular, that the breaking points on the wave profile may shift from the zerocrossing level. The wave steepening happens in a different way if the density jump is placed near the middle of the water bulk: then the wave deformation is almost symmetrical and two phases appear where the wave breaks.

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We have investigated the spatiotemporal properties of solitons generated on the shallow water surface over a background of a large-scale mode in a hydrodynamic resonator when it is forced near the second frequency mode. We have used the space-time diagrams to highlight the spatiotemporal dynamics of nonlinear fields for two solitons colliding in a resonator and compared them to those of solitons occurring in an unbounded system. A state diagram of experimentally observed modes for different values of the excitation parameters has been obtained. In particular, we have evidenced period doubling and the multistability of nonlinear waves excited in the resonator. For a theoretical description of these experimental results, we have developed a phenomenological model, which leads to amplitude and phase equations of a soliton propagating over the background of a harmonic wave. To reproduce experimental results on the multistability, we have supplemented our analysis with a numerical simulation of a modified system of Boussinesq equations for shallow water, taking into account the dissipation effect