We revisit the complex interplay between the Raman-induced frequency shift (RIFS) and the effect of self-steepening (SS) in the propagation of solitons, and in the framework of an equation that ensures strict conservation of the number of photons. The generalized nonlinear Schrödinger equation (GNLSE) is shown to severely fail in preserving the number of photons for sub-100-fs solitons, leading to a large overestimation of the frequency shift. Furthermore, when considering the case of a frequency-dependent nonlinear coefficient, the GNLSE also fails to provide a good estimation of the time shift experienced by the soliton. We tackle these shortcomings of the GNLSE by resorting to the recently introduced photon-conserving GNLSE (pcGNLSE) and study the interplay between the RIFS and self-steepening. As a result, we make apparent the impact of higher-order nonlinearities on short-soliton propagation and propose an original and direct method for the estimation of the second-order nonlinear coefficient.

中文翻译：

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在严格的光子数守恒下重新审视光纤中的孤子动力学

我们重新审视了拉曼引起的频移 (RIFS) 与孤子传播中自陡峭 (SS) 的影响之间的复杂相互作用，并在确保光子数量严格守恒的方程的框架内。广义非线性薛定谔方程 (GNLSE) 在保留亚 100-fs 孤子的光子数量方面严重失败，导致对频移的高估。此外，当考虑与频率相关的非线性系数的情况时，GNLSE 也无法提供对孤子经历的时移的良好估计。我们通过采用最近引入的光子守恒 GNLSE (pcGNLSE) 来解决 GNLSE 的这些缺点，并研究 RIFS 和自陡峭之间的相互作用。因此，