Mathematical, numerical and experimental study of solitary waves

Abstract

The note discusses the motion of solitary waves on the free surface of a layer of water. The rigorous results for the existence of solitary-wave solutions of exact governing equations are given. To generate such surface waves, a moving bump placed at the bottom or a pressure source on the free surface is used. A model equation, called forced Korteweg–de Vries (FKdV) equation, is numerically studied and multi- solitary- wave solutions are obtained. Then, the numerical solutions are compared with experimental results using a water tank with a moving bump at the bottom.