Mathematical Theory of Water Waves

Abstract

The water-wave problem is the study of the two- and threedimensional irrotational flow of a perfect fluid bounded above by a free surface subject to the forces of gravity and surface tension. It is a paradigm for most modern methods in nonlinear functional analysis and nonlinear dispersive wave theory. Its mathematical study calls upon many different approaches, as iteration methods, bifurcation theory, dynamical systems theory, complex variable methods, PDE methods, the calculus of variations, positive operator theory, topological degree theory, KAM theory, and symplectic geometry.