On one class of systems of Lax-type equations
The authors consider the Lax-type system \[ \begin{cases} [a(x),\gamma(x)]=0, & x\in[0,l], \\ \gamma'(x)=i[a(x),\sigma_2], & x\in[0,l], \\ \gamma(0)=\gamma^+, \\ \end{cases} \eqno(1) \] where \(a(x),\) \(\gamma(x),\) \(\sigma_2,\) and \(\gamma^+\) are self-adjoint \(n\times n\) matrices, and \([A,B]=AB-BA\) is a commutator of the matrices \(A,B\in \mathbb{C}^{n\times n}.\) All solutions of (1) are given for some cases, in particular, for the cases of a linear and a quadratic dependence of \(a(x)\) on \(\gamma(x)\).
scientific article; zbMATH DE number 6355169