This Brief Report is devoted to the study of the solitary surface wave rotating in the azimuthal direction, arising during water drainage from a cylindrical reservoir, when shallow flow conditions are reached. The linear dependence between the wave speed and its amplitude is shown to be similar to that expected from the classical Korteweg-de Vries equation.

In the propagation and evolution of sea waves, previous studies pointed out that occurrence freak wave height is significantly related to quasi-resonant four-wave interaction in modulated waves. From numerical--experimental study over an uneven bottom, nonlinear effect caused by bathymetry change also contributes extreme events unidirectional To comprehensively analyse two-dimensional wavefield...

This paper is devoted to the study of a recently derived periodic shallow water equation. We discuss in detail the blow-up scenario of strong solutions and present several conditions on the initial profile, which ensure the occurrence of wave breaking. We also present a family of global weak solutions, which may be viewed as global periodic shock waves to the equation under discussion.

A general method for the derivation of asymptotic nonlinear shallow water and deep water models is presented. Starting from a general dimensionless version of the water-wave equations, we reduce the problem to a system of two equations on the surface elevation and the velocity potential at the free surface. These equations involve a Dirichlet-Neumann operator and we show that all the asymptotic...

is an extensively studied nonlinear equation. It first appeared as an abstract biHamiltonian partial differential equation in an article of Fuchssteiner and Fokas [39] but did not receive much attention until Camassa and Holm [15] (see also [16]) derived it as a nonlinear wave equation that models unidirectional wave propagation on shallow water and discovered its rich mathematical structure. I...

Abstract In this article, through the Hirota bilinear method and long wave limit method, based on N-solitons, we construct multiple lump solutions of generalized (3+1)-dimensional Hirota–Satsuma–Ito equation. Furthermore, to enhance our understanding obtained, further elucidate physical implications these with three-dimensional two-dimensional graphs. The obtained might have practical applicati...