Hamiltonian structures related to a new spectral problem (Q918000)

The spectral problem \(\phi_ x=\left( \begin{matrix} -i\lambda +r\\ p\end{matrix} \begin{matrix} \lambda q\\ i\lambda -r\end{matrix} \right)\phi\) was discussed by \textit{A. Roy Chowdhury} and \textit{Swapra Roy} [Int. J. Theor. Phys. 25, 207-213 (1986; Zbl 0592.58021)]. They tried to get the isospectral flows related to the spectral problem and to find the Hamiltonian structures, but they did not accomplish this. The present author shows that this can be done concisely by means of Trace Identity of \textit{Guizhang Tu} [J. Math. Phys. 30, No.2, 330-338 (1989; Zbl 0678.70015)].