The direct Zakharov–Shabat scattering problem has recently gained significant attention in various applications of fiber optics. The development of accurate and fast algorithms with low computational complexity to solve the Zakharov–Shabat problem (ZSP) remains an urgent problem in optics. In this Letter, a fourth-order multi-exponential scheme is proposed for the Zakharov–Shabat system. The construction of the scheme is based on a fourth-order three-exponential scheme and Suzuki factorization. This allows one to apply the fast algorithms with low complexity to calculate the ZSP for a large number of spectral parameters. The scheme conserves the quadratic invariant for real spectral parameters, which is important for various telecommunication problems related to information coding.

中文翻译：

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求解Zakharov-Shabat直接散射问题的保守多指数方案

Zakharov-Shabat直接散射问题最近在光纤的各种应用中引起了广泛关注。为了解决Zakharov-Shabat问题（ZSP），开发具有低计算复杂度的准确，快速的算法仍然是光学领域的紧迫问题。在这封信中，为Zakharov-Shabat系统提出了四阶多指数方案。该方案的构建基于四阶三指数方案和Suzuki分解。这样一来，人们就可以应用低复杂度的快速算法来计算大量频谱参数的ZSP。该方案保留了真实频谱参数的二次不变性，这对于与信息编码有关的各种电信问题很重要。