Two-dimensional periodic surface waves propagating under the combinedinfluence of gravity and surface tension on water of finite depth areconsidered. Within the framework of small-amplitude waves, we find the exactsolutions of the nonlinear differential equation system which describes theparticle motion in the considered case, and we describe the possible particletrajectories. The required computations involve elliptic integrals of the firstkind, the Legendre normal form and a solvable Abel differential equation of thesecond kind. Some graphs of the results are included.
展开▼
