Search

This article theoretically investigates the diffraction and radiation of an array of coaxial double-layer porous cylindrical structures placed on a porous seabed. The array of the structures is considered a bottom-mounted cylindrical structure with vanishing thickness. Under the assumption of a small amplitude wave theory, the hydrodynamic characteristics of an array of coaxial double-layer porous cylindrical structures are investigated. The diffraction and the radiation of the structure array are investigated using the eigenfunction expansion method, Bessel function addition theory, and Darcy's law. Analytical expressions for the velocity potentials and free-surface elevations for the diffraction and radiation of the structural array are derived. Finally, the unknown coefficients of the velocity potential are determined using the matching feature function method. After completing the validation, a detailed parameter study is conducted on the structural array, and the hydrodynamic characteristics of the structure array under the influence of different parameters are discussed and explained. Taking the horizontal layout as an example, the results show that in addition to the influence of structure parameters such as porosity, the radius ratio, and the cylinder distance on the hydrodynamic presence of the array of porous structures, the number of cylinders has a greater influence on the hydrodynamic characteristics of the array of porous structures. The calculation results of the diffraction and radiation of an array of porous structures placed on a porous seabed are closer to the actual situation, which can better understand the interaction between waves and porous structure and provide effective theoretical reference for engineers to design ocean structures. [ABSTRACT FROM AUTHOR]

A generalized fractional trace identity and Hamiltonian structure of the fractional soliton equation hierarchy are presented by using the modified Riemann-Liouville derivative and exterior derivatives of fractional orders. Example of the fractional Kaup Newell (KN) soliton equation hierarchy and Hamiltonian system are considered, which is a new integrable hierarchy and possesses Hamiltonian structure. [ABSTRACT FROM AUTHOR]

Starting from a discrete spectral problem, we derive a hierarchy of nonlinear discrete equations which include the Ablowitz-Ladik (AL) equation. We analytically study the discrete rogue-wave (DRW) solutions of AL equation with three free parameters. The trajectories of peaks and depressions of profiles for the first- and second-order DRWs are produced by means of analytical and numerical methods. In particular, we study the solutions with dispersion in parity-time ( PT) symmetric potential for Ablowitz-Musslimani equation. And we consider the non-autonomous DRW solutions, parameters controlling and their interactions with variable coefficients, and predict the long-living rogue wave solutions. Our results might provide useful information for potential applications of synthetic PT symmetric systems in nonlinear optics and condensed matter physics.