HIGHER ORDER KORTEWEG-DE VRIES MODELS FOR INTERNAL WAVES

Abstract

By using asymptotic methods, evolution equation is derived for the internal waves in density stratified fluid. This evo- lution equation arise as a solvability condition. A higher-order extension of the familiar Korteweg-de Vries equation is produced for internal waves in a density stratified flow with a free surface. All coefficients of this extended Korteweg-de Vries equation are expressed via integrals of the modal function for the linear theory of long internal waves.