This paper considers the Radhakrishnan — Kundu — Laksmanan (RKL) equation to analyze dispersive nonlinear waves in polarization-preserving fibers. The Cauchy problem for this equation cannot be solved by the inverse scattering transform (IST) and we look for exact solutions of this equation using the traveling wave reduction. The Painlevé analysis for the traveling wave reduction of the RKL equation is discussed. A first integral of traveling wave reduction for the RKL equation is recovered. Using this first integral, we secure a general solution along with additional conditions on the parameters of the mathematical model. The final solution is expressed in terms of the Weierstrass elliptic function. Periodic and solitary wave solutions of the RKL equation in the form of the traveling wave reduction are presented and illustrated.

中文翻译：

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Radhakrishnan-Kundu-Lakshmanan方程的Painlevé分析和行波减少的解决方案

本文考虑了Radhakrishnan-Kundu-Laksmanan（RKL）方程来分析保偏光纤中的色散非线性波。该方程的柯西问题不能通过逆散射变换（IST）求解，我们使用行波约简来寻找该方程的精确解。讨论了RKL方程行波约简的Painlevé分析。恢复了针对RKL方程的行波减小的第一积分。使用此第一个积分，我们可以在数学模型的参数上确保通用解以及附加条件。最终解以Weierstrass椭圆函数表示。提出并举例说明了RKL方程的行波和孤波解。