system of integro-differential equations
Dipole approximation for the problem on nonlinear waves generation by an embedded sphere
The author studies nonstationary surface waves in the presence of an embedded sphere. The Cauchy-Poisson problem with nonlinear boundary conditions on the free boundary is reduced to a system of integro-differential equations which describe the free boundary and potential function on it. It is shown that the leading term in asymptotic expansion with respect to the fluid depth can be represented as a dipole whose moment depends on the radius of the sphere, on its velocity, of the shape of wave surface, and on the fluid velocity on the free surface.
scientific article; zbMATH DE number 1682201