利用非线性薛定谔方程的椭圆解形成深水三维表面波
Formation of three-dimensional surface waves on deep-water using elliptic solutions of nonlinear Schrödinger equation
摘要：
本文综述了深水三维波浪的研究进展。三种形式的三维性，即斜，被迫和自发的类型。通过三次非线性薛定谔方程给出了三维波的另一种形式。利用Weierstrass椭圆$\wp$函数求出了三次非线性薛定谔方程的周期解.结果表明，解的分类依赖于边界条件，波数和频率。对于某些参数，Weierstrass $\wp$函数被简化为周期、双曲或Jacobi椭圆函数。它表明，这些解决方案中的一些没有任何物理意义。本文还得到了三次非线性薛定谔方程在风强迫作用下的解析解，从而解释了海洋深水表面上的波群是如何产生的。在这种情况下，从风到波浪，对能量传递参数的依赖性使波群要么最初增长并最终消散，要么简单地随时间衰减或增长。
英文摘要：
A review of three-dimensional waves on deep-water is presented. Three forms of three dimensionality, namely oblique, forced and spontaneous type, are identified. An alternative formulation for these three-dimensional waves is given through cubic nonlinear Schrödinger equation. The periodic solutions of the cubic nonlinear Schrödinger equation are found using Weierstrass elliptic $\wp$ functions. It is shown that the classification of solutions depends on the boundary conditions, wavenumber and frequency. For certain parameters, Weierstrass $\wp$ functions are reduced to periodic, hyperbolic or Jacobi elliptic functions. It is demonstrated that some of these solutions do not have any physical significance. An analytical solution of cubic nonlinear Schrödinger equation with wind forcing is also obtained which results in how groups of waves are generated on the surface of deep water in the ocean. In this case the dependency on the energy-transfer parameter, from wind to waves, make either the groups of wave to grow initially and eventually dissipate, or simply decay or grow in time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
