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Explicit solutions of Schrödinger and KdV equations in terms of square roots of the generalised matrix eigenvalues (2205.13463v1)
Published 26 May 2022 in math.CA, math-ph, math.DS, math.MP, and nlin.SI
Abstract: In this paper, we consider matrix Schr\"odinger equation, dynamical Schr\"odinger equation and matrix KdV. We construct their explicit solutions using our GBDT version of B\"acklund--Darboux transformation and square roots of the generalised matrix eigenvalues. A separate section is dedicated to several examples including the case of strongly singular potentials.
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