Effect of capillarity on fourth-order nonlinear evolution equations for two Stokes wave trains in deep water

Abstract

Fourth-order nonlInear evalution equations, which are good starting point for the study of nonlinear water waves, are derived for a deep-water surface capillary gravity wave packet in the presence of a second wave packet. Stability analysis is made for a uniform wave train in the presence of a second uniform wave train. Graphs are plotted for maximum growth rate of instability and for wave number at marginal stability against wave steepness. Significant deviations are noticed from the results obtained from the third-order evolution equations which consist of two coupled nonlinear Schrodinger equations.