Time-Dependent Analytic Solutions for Water Waves above Sea of Varying Depths

Abstract

We investigate a hydrodynamic equation system which—with some approximation—is capable of describing the tsunami propagation in the open ocean with the time-dependent self-similar Ansatz. We found analytic solutions of how the wave height and velocity behave in time and space for constant and linear seabed functions. First, we study waves on open water, where the seabed can be considered relatively constant, sufficiently far from the shore. We found original shape functions for the ocean waves. In the second part of the study, we also consider a seabed which is oblique. Most of the solutions can be expressed with special functions. Finally, we apply the most common traveling wave Ansatz and present relative simple, although instructive solutions as well.

Lump-Type Solutions, Mixed Solutions and Rogue Waves for a (3+1)-Dimensional Variable-Coefficients Burgers Equation

“…Nonlinear evolution equations (NLEEs) have gained increasing attention in the field of nonlinear science due to their many applications in various fields, such as fluid mechanics [1,2], plasma physics [3], optics [4], biology [5], and condensed matter physics [6]. The most important of these studies are meant to obtain soliton solutions.…”

Solitary Wave Propagation of the Generalized Rosenau–Kawahara–RLW Equation in Shallow Water Theory with Surface Tension

“…Flooding, heat waves, early spring arrival, sea-level rise, glacier melting, coral reef bleaching, and disease contagions are the present-day results of climate change [3][4][5][6][7]. Nevertheless, these giant waves can constitute alternative energy resources for near-future applications if the essential technology is implemented [8][9][10][11][12].…”