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In this paper, we consider matrix Schr\"odinger equation, dynamicalSchr\"odinger equation and matrix KdV. We construct their explicit solutionsusing our GBDT version of B\"acklund--Darboux transformation and square rootsof the generalised matrix eigenvalues. A separate section is dedicated toseveral examples including the case of strongly singular potentials.

Explicit solutions of Schr\"odinger and KdV equations in terms of square roots of the generalised matrix eigenvalues