We investigate the influence of spatially homogeneous multiplicative noise on propagating dissipative solitons (DSs) of the cubic complex Ginzburg-Landau equation stabilized by nonlinear gradient terms. Here we focus on the nonlinear gradient terms, in particular on the influence of the Raman term and the delayed nonlinear gain. We show that a fairly small amount of multiplicative noise can lead to a change in the mean velocity for such systems. This effect is exclusively due to the presence of the stabilizing nonlinear gradient terms. For a range of parameters we find a velocity change proportional to the noise intensity for the Raman term and for delayed nonlinear gain. We note that the dissipative soliton decreases the modulus of its velocity when only one type of nonlinear gradient is present. We present a straightforward mean field analysis to capture this simple scaling law. At sufficiently high noise strength the nonlinear gradient stabilized DSs collapse.

中文翻译：

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乘性噪声会引起传播性耗散孤子的速度变化

我们研究了空间均匀乘性噪声对由非线性梯度项稳定的三次复数Ginzburg-Landau方程的传播耗散孤子（DSs）的影响。在这里，我们关注非线性梯度项，特别是拉曼项和延迟非线性增益的影响。我们表明，相当数量的乘法噪声会导致此类系统的平均速度发生变化。这种影响完全是由于稳定的非线性梯度项的存在。对于一系列参数，我们发现速度变化与拉曼项和延迟非线性增益的噪声强度成正比。我们注意到，当仅存在一种类型的非线性梯度时，耗散孤子会降低其速度模量。我们提出了一种简单的均值场分析方法来捕获这种简单的定标定律。在足够高的噪声强度下，非线性梯度稳定的DS会崩溃。