Abstract
We construct three classes of higher-order Darboux transformations for Schrödinger equations with quadratically energy-dependent potentials by means of generalized Wronskian determinants. Particular even-order cases reduce to the Darboux transformation for conventional (energy-independent) potentials. Our construction is based on an adaptation of the results for coupled Korteweg–de Vries equations [N. V. Ustinov and S. B. Leble, J. Math. Phys. 34, 1421 (1993)].
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