Basic Studies on the Qauntumzation of Nonlinear Coastal Waves

近年来人们认识到，浅水波是由一种以孤子为基元激发的动态相干结构组成的。为了用孤子模表示波，对由KdV方程导出的Stokes波和孤子进行量子化，得到能量分布函数。在此基础上，提出了随机孤子的统计理论。1）对于Stokes波的量子化，由Stokes波的哈密顿量导出的Schroedinger方程的解具有波能量分布函数。从浅水波的动力学相干结构出发，提出了随机孤子的统计理论。利用绪方波浪观测站的波浪资料，对各种情况下的波浪进行了应用。3）对于Ursell数大于10的非线性波，孤波在波剖面上的适用性很好，以及包括破碎波在内的波浪。在不同的波浪条件下，得到了三种孤子本征值分布函数，它们在浅水中的传播是保守的水作为孤子模式。将理论能量分布函数与观测值进行了比较，两者吻合较好。

It has recently been recongnized that waves in shallow water are composed of a dynamic coherent structure in which solitons are elementary excitation. To formulate the waves with soliton modes, qauntumzation of Stokes waves and solitons which are deduced from the KdV equation is made and energy distribution function is obtained. Based on the formulation, a statistical theory of random solitons is proposed. The main results are summarized as:1) For the qauntumzation of Stokes waves, solutions to the Schroedinger equation which was derived from the Hamiltonian of Stokes waves were obtained to have wave energy distribution functions. Similar distribution functions of solitons were obtained from the KdV equation.2) From the view point of dynamic coherent structures of the waves in shallow water, a statistical theory of random solitons was proposed. Its applications to waves in various conditions were made using wave data obtained at Ogata Wave Observatory.3) Applicability of the solitons in wave profiles is very good for the nonlinear waves having greater Ursell numbers than 10, as well as waves including breaking waves.4) Three types of soliton eigenvalue distribution functions were obtained for various wave conditions and they are conservative in propagation of the waves in shallow water as soliton modes. The theoretical energy distribution function was compared with the observed ones with good agreement.