Explicit solutions of Schrödinger and KdV equations in terms of square roots of the generalised matrix eigenvalues

Abstract

In this paper, we consider matrix Schrödinger equation, dynamical Schrödinger equation and matrix KdV. We construct their explicit solutions using our GBDT version of Bäcklund--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.

We develop further several results from arXiv:1701.08011 and arXiv:1010.4902

References in corpus (2)

• Solvable rational extensions of the isotonic oscillator
• Dressing for generalised linear Hamiltonian systems depending rationally on the spectral parameter and some applications