Abstract
This paper continues a series of papers in which simultaneous \(2\times 2\) matrix solutions of two scalar evolution equations,which are analogs of time-dependent Schrödinger equations, were constructed. In theconstructions in the present paper, these equations correspond to the Hamiltonian system \(H^{2+2+1}\) —one of the representatives of the hierarchyof degenerations of the isomonodromic Garnier system. The mentioned hierarchy was described byH. Kimura in 1986. In terms of solutions of linear systems of differential equations in the methodof isomonodromic deformations, the consistency condition for which is the Hamiltonian equationsof the \(H^{2+2+1}\) system, the constructed simultaneous matrixsolutions of analogs of time-dependent Schrödinger equations are written out explicitly inthis paper.
