论文标题
在强制非线性schrödinger方程中的波群的扩增
Amplification of wave groups in the forced nonlinear Schrödinger equation
论文作者
论文摘要
在许多物理环境中，特别是包括深水波，通常使用非线性Schrödinger方程来研究一个空间维度的调节不稳定性。感兴趣的主要解决方案是用作波数据包模型的孤子和呼吸器。特别是，尤其是三分之一的呼吸器作为流氓浪潮的模型。在本文中，我们在非线性schrödinger方程中添加了线性生长项，以模拟传播波群的扩增。这是由于对风波的应用而动机，但是这种强迫的非线性schrödinger方程可能具有更大的适用性。我们描述了一系列数值模拟，在没有强迫术语的情况下会产生孤子和/或呼吸。我们发现，总体而言，强迫术语的效果是偏爱产生的孤子，其振幅比呼吸器产生的线性增长速度的两倍增长。
In many physical contexts, notably including deep water waves, modulation instability in one space dimension is often studied using the nonlinear Schrödinger equation. The principal solutions of interest are solitons and breathers which are adopted as models of wave packets. The Peregrine breather in particular is often invoked as a model of a rogue wave. In this paper we add a linear growth term to the nonlinear Schrödinger equation to model the amplification of propagating wave groups. This is motivated by an application to wind-generated water waves, but this forced nonlinear Schrödinger equation has potentially much wider applicability. We describe a series of numerical simulations which in the absence of the forcing term would generate solitons and/or breathers. We find that overall the effect of the forcing term is to favour the generation of solitons with amplitudes growing at twice the linear growth rate over the generation of breathers.
