We study the propagation of ultrashort pulses in optical fiber with gain and positive (or normal) quartic dispersion by self-similarity analysis of the modified nonlinear Schrödinger equation. We find an exact asymptotic solution, corresponding to a triangle-like ${T^{4/3}}$ intensity profile, with a ${T^{1/3}}$ chirp, which is confirmed by numerical simulations. This solution follows different amplitude and width scaling compared to the conventional case with quadratic dispersion. We also suggest, and numerically investigate, a fiber laser consisting of components with positive quartic dispersion that emits quartic self-similar pulses.

中文翻译：

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光脉冲在具有正四次色散的光纤中的自相似传播。

我们通过修正非线性Schrödinger方程的自相似性分析研究具有增益和正（或正常）四次色散的超短脉冲在光纤中的传播。我们找到了一个精确的渐近解，它对应于三角形的$ {T ^ {4/3}} $强度分布，并具有$ {T ^ {1/3}} $线性调频，这已通过数值模拟得到了证实。与具有二次色散的常规情况相比，该解决方案遵循不同的幅度和宽度缩放比例。我们还建议并进行数值研究，该光纤激光器由四次正色散为正的分量组成，并发出四次自相似脉冲。