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

Abstract

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

42 pages, 27 figures, 1 table, 48 references. Other author's papers can be downloaded at http://www.denys-dutykh.com/

References in corpus (5)

• Shock waves in dispersive hydrodynamics with non-convex dispersion
• Hamiltonian formulation of the extended Green-Naghdi equations
• The Whitham Equation with Surface Tension
• On weakly singular and fully nonlinear travelling shallow capillary-gravity waves in the critical regime
• Algebraic method for constructing singular steady solitary waves: A case study

Cited by in corpus (3)

• Investigating overtaking collisions of solitary waves in the Schamel equation
• Well-posedness and derivative blow-up for a dispersionless regularized shallow water system
• On the blow-up scenario for some modified Serre-Green-Naghdi equations