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Direct scattering transform of nonlinear wave fields with solitons may leadto anomalous numerical errors of soliton phase and position parameters. Withthe focusing one-dimensional nonlinear Schr\"odinger equation serving as amodel, we investigate this fundamental issue theoretically. Using the dressingmethod we find the landscape of soliton scattering coefficients in the plane ofthe complex spectral parameter for multi-soliton wave fields truncated within afinite domain, allowing us to capture the nature of particular numericalerrors. They depend on the size of the computational domain $L$ leading to acounterintuitive exponential divergence when increasing $L$ in the presence ofa small uncertainty in soliton eigenvalues. In contrast to classical textbooks,we reveal how one of the scattering coefficients loses its analyticalproperties due to the lack of the wave field compact support in case of $L \to\infty$. Finally, we demonstrate that despite this inherit direct scatteringtransform feature, the wave fields of arbitrary complexity can be reliablyanalysed.

Direct scattering transform: catch soliton if you can