标题： 本杰明-费尔不稳定性引起的最大振幅增加的研究 显示英文标题

标题： Investigation of the maximum amplitude increase from the Benjamin-Feir instability

摘要： 非线性薛定谔（NLS）方程用于模拟水动力实验室中波槽中的表面波。 对线性化NLS方程的分析表明，其具有小振幅调制的谐波解由于所谓的本杰明-费尔不稳定性，有指数增长的趋势。 为了详细研究这种增长，我们将NLS方程的线性化解与一个完全非线性的精确解联系起来，称为有限背景上的孤子。 结果表明，在不稳定性范围内，最大振幅增加是有限的，最多可达初始振幅的三倍。 显示英文摘要

摘要： The Nonlinear Schr\"odinger (NLS) equation is used to model surface waves in wave tanks of hydrodynamic laboratories. Analysis of the linearized NLS equation shows that its harmonic solutions with a small amplitude modulation have a tendency to grow exponentially due to the so-called Benjamin-Feir instability. To investigate this growth in detail, we relate the linearized solution of the NLS equation to a fully nonlinear, exact solution, called soliton on finite background. As a result, we find that in the range of instability the maximum amplitude increase is finite and can be at most three times the initial amplitude.