Solitary wave solutions and their interactions for fully nonlinear water waves with surface tension in the generalized Serre equations

摘要

Some effects of surface tension on fully-nonlinear, long, surface water wavesare studied by numerical means. The differences between various solitary wavesand their interactions in subcritical and supercritical surface tension regimesare presented. Analytical expressions for new peaked travelling wave solutionsare presented in the case of critical surface tension. The numericalexperiments were performed using a high-accurate finite element method based onsmooth cubic splines and the four-stage, classical, explicit Runge-Kutta methodof order four.