波浪ソリトン群とその統計理論

Abstract

In general, waves in shallow water may be characterized by nonlinearity and randomnessthrough the governing equations of the waves. Especially waves in very shallow water may beexpressed dynamically by soliton modes, retaining a dynamical sequence as a train of solitons, random multi-solitons. A statistical theory of the multi-solitons is proposed based on theconservative property of the eigenvalues of solitons, by introducing a random variable inpropagation of the multi-solitons.The conservative property of the solitons is examined by observed data of waves at OgataCoast to find distribution functions of eigenvalues for various conditions of waves. And applicationof the statistical theory to the wave data shows good agreement with the data of soliton statistics, so that we conclude that random waves in very shallow water can be treated practically as a trainof solitons having a coherent structure of random multi-solitons.