Internal Solitary Waves in Two-Layer Fluids at Near-Critical Situation

摘要

A new model equation describing weakly nonlinear long internalwaves at the interface between two thin layers of differentdensity is derived for the specific relationships between thedensities, layer thicknesses and surface tension between thelayers. The equation derived and dubbed here the Gardner–Kawahara equation represents a natural generalisation of thewell-known Korteweg–de Vries (KdV) equation containing thecubic nonlinear term as well as fifth-order dispersion term.Solitary wave solutions are investigated numerically andcategorised in terms of two dimensionless parameters, the wavespeed and fifth-order dispersion. The equation derived may beapplicable to wave description in other media.