Analytic rogue wave-type solutions for the generalized (2+1)-dimensional Boussinesq Equation

Based on the Hirota bilinear form of the generalized (2+1)-dimensional Boussinesq equation, which can be expressed as the shallow water wave mechanism appearing in fluid mechanics, we applied the new polynomial functions to construct the rational solutions and rogue wave-type solutions. Next, the system parameters control on the rational solutions and rogue wave-type solutions were also shown. As a result, we found the following basic facts: (i) these parameters may affect the wave shapes, amplitude, and bright/dark for this considered equation, (ii) the solitary wave interaction rogue waves and triplet rogue wave-type solutions can be viewed on [Formula: see text], [Formula: see text], and [Formula: see text] planes, respectively. Their nonlinear dynamic behaviors were presented by numerical simulation of the 2D- and 3D-plots.

Experimental Investigation on Solitary Wave Interaction With Vertical Porous Barriers

Tsunami waves pose a threat to the coastal zone, and numerous studies have been carried out in the past to understand them. Solitary waves have been extensively used in research because they approximate certain important characteristics of tsunami waves. The present study focusses on the interaction and run-up of solitary waves on coastal protection structures in the form of thin, rigid vertical porous barriers with special attention given to the degree of energy dissipation. To understand the physics of energy dissipation, solitary wave interaction with a porous barrier has been studied from the viewpoint of energy balance. Based on this, a relationship for the wave energy dissipation has been developed. The experimental data show that the plate porosity that gives the optimal energy dissipation lies within the 10–20% range. From the experiments, the phase shift that the solitary wave undergoes upon interaction with the porous barrier models has also been recorded. In addition, a formula is proposed for maximum wave run-up on the porous barrier, which should be useful in the planning, design, construction, and maintenance of coastal protection structures.

Consistent Particle Method Simulation of Solitary Wave Interaction with a Submerged Breakwater

This paper presents a numerical study of the solitary wave interaction with a submerged breakwater using the Consistent Particle Method (CPM). The distinct feature of CPM is that it computes the spatial derivatives by using the Taylor series expansion directly and without the use of the kernel or weighting functions. This achieves good numerical consistency and hence better accuracy. Validated by published experiment data, the CPM model is shown to be able to predict the wave elevations, profiles and velocities when a solitary wave interacts with a submerged breakwater. Using the validated model, the detailed physics of the wave breaking process, the vortex generation and evolution and the water particle trajectories are investigated. The influence of the breakwater dimension on the wave characteristics is parametrically studied.