The propagation of internal solitary waves (ISWs) flowing over the submerged topography is a strongly nonlinear process. To extract the dynamic characteristics of this process, an improved dynamic mode decomposition method is proposed in this paper, which is named piecewise dynamic mode decomposition (PDMD). The innovation of this method is to split the entire evolution process into several quasi-linear segments before modal analyzing to reduce the requirements on the spatial and temporal resolutions of input measured data. A feasible criterion for linearity is introduced by combining the proper orthogonal decomposition method, which is an important basis of PDMD. The data used in the analysis are provided by the experiments conducted in a stratified wave tank. The experimental conditions are set as ISWs flowing over two typical bottom topographies. The interfacial displacement and flow field information are analyzed as the measured data. Through reconstruction and modal analysis of experimental data, the effectiveness and flexibility of PDMD are verified for the ISW problem. The physical meaning of segmentation points can be explained. Based on the results of model decomposition, the main propagation characteristics of ISWs under different conditions are discussed. The evolution of the waveform or local flow phenomena can be simplified to the superposition of linear modes with frequency information.

In this paper, we consider the (2+1)-dimensional Ito equation, which was introduced by Ito. By considering the Hirota’s bilinear method, and using the positive quadratic function, we obtain some lump solutions of the Ito equation. In order to ensure rational localization and analyticity of these lump solutions, some sufficient and necessary conditions are provided on the parameters that appeared in the solutions. Furthermore, the interaction solutions between lump solutions and the stripe solitons are discussed by combining positive quadratic function with exponential function. Finally, the dynamic properties of these solutions are shown via the way of graphical analysis by selecting appropriate values of the parameters.

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This paper is concerned with the interaction of an internal solitary wave (ISW) at the interface of two-layer fluid and the free surface wave on top of the upper layer. It is based on the potential flow theory since internal waves are associated with large Reynolds numbers. The potential flows in the upper layer and lower layer are modeled using a multi-domain boundary element method (MDBEM). The computational model is validated with the experimental results for the profile and speed of the internal wave. The MDBEM is suitable for the simulation of ISW in both small and large density jump stratified fluid system. The wave velocity is compared with the approximate analytical theory for various ratios of the fluid densities of the two layers. In addition, the amplitude, velocity and profile of the surface wave induced by ISWs are investigated. The free surface displacement is opposite to that of the interface, and the amplitude of the surface wave increases with the amplitude and density jump. The surface wave induced by an ISW can be soliton-like wave, propagating with the constant speed of the ISW and maintaining its profile.