Soliton and breather solutions of the nonlinear Schrödinger equation (NLSE) are known to model localized structures in nonlinear dispersive media such as on the water surface. One of the conditions for an accurate propagation of such exact solutions is the proper generation of the exact initial phase-shift profile in the carrier wave, as defined by the NLSE envelope at a specific time or location. Here, we show experimentally the significance of such initial exact phase excitation during the hydrodynamic propagation of localized envelope solitons and breathers, which modulate a plane wave of constant amplitude (finite background). Using the example of stationary black solitons in intermediate water depth and pulsating Peregrine breathers in deep water, we show how these localized envelopes disintegrate while they evolve over a significant long distance when the initial phase shift is zero. By setting the envelope phases to zero, the dark solitons will disintegrate into two gray-type solitons and dispersive elements. In the case of the doubly localized Peregrine breather the maximal amplification is considerably retarded; however, locally, the shape of the maximal focused wave measured together with the respective signature phase-shift are almost identical to the exact analytical Peregrine characterization at its maximal compression location. The experiments, conducted in large-scaled shallow-water as well as deep-water wave facilities, are in very good agreement with NLSE simulations for all cases.

中文翻译：

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恒背景平面波上孤子的相抑制流体力学

已知非线性Schrödinger方程（NLSE）的孤子和通气解可以对非线性分散介质（例如水表面）中的局部结构进行建模。此类精确解的精确传播的条件之一是在特定时间或位置由NLSE包络线定义的载波中正确生成准确的初始相移曲线。在这里，我们通过实验证明了在局域包络孤子和通气孔的流体动力传播过程中，这种初始精确相位激励的重要性，后者调制了恒定振幅（有限背景）的平面波。以中等水深的静止黑色孤子和深水中的脉冲游eg呼吸器为例，我们展示了当初始相移为零时，这些局部包络如何在相当长的距离内演化时解体。通过将包络相位设置为零，深色孤子将分解为两个灰色孤子和色散元素。如果使用双重定位的百富勤呼吸器，则最大放大率会大大降低；然而，局部地，所测量的最大聚焦波的形状以及相应的特征相移几乎与在其最大压缩位置处的精确分析百富勤特性相同。在大型浅水和深水波浪设施中进行的实验与所有情况下的NLSE模拟都非常吻合。深色孤子将分解为两个灰色孤子和色散元素。如果使用双重定位的百富勤呼吸器，则最大放大率会大大降低；然而，局部地，所测量的最大聚焦波的形状以及相应的特征相移几乎与在其最大压缩位置处的精确分析百富勤特性相同。在大型浅水和深水波浪设施中进行的实验与所有情况下的NLSE模拟都非常吻合。深色孤子将分解为两个灰色孤子和色散元素。如果使用双重定位的百富勤呼吸器，则最大放大率会大大降低；然而，局部地，所测量的最大聚焦波的形状以及相应的特征相移几乎与在其最大压缩位置处的精确分析百富勤特性相同。在大型浅水和深水波浪设施中进行的实验与所有情况下的NLSE模拟都非常吻合。所测量的最大聚焦波的形状以及各自的特征相移几乎与在其最大压缩位置处的精确分析百富勤特性完全相同。在大型浅水和深水波浪设施中进行的实验与所有情况下的NLSE模拟都非常吻合。所测量的最大聚焦波的形状以及各自的特征相移几乎与在其最大压缩位置处的精确分析百富勤特性完全相同。在大型浅水和深水波浪设施中进行的实验与所有情况下的NLSE模拟都非常吻合。