Randomized trial demonstrates a new criterion for solvability in matrix soliton equations, suggesting advancements in solution methods.
A criterion for the solvability of a holomorphic Cauchy problem for a certain class of matrix soliton equations is proved in terms of a scattering transform defined in a new way. For the equations under consideration, a method is indicated for constructing holomorphic solutions using the Zakharov-Shabat dressing method for the zero solution, as well as the possibility of extending the solutions with respect to the spatial variable to globally meromorphic functions.
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M. A. Shumkin (2026) studied this question.
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