Quadratic bundle and nonlinear equations

A class of nonlinear evolution equations solvable by means of the inverse scattering problem method for the quadratic bundle
$$L_\lambda\psi=\left[i\begin{pmatrix}1&0\\0&-1\end{pmatrix}\frac{d}{dx}+\lambda\begin{pmatrix}0&q(x)\\p(x)&0\end{pmatrix}-\lambda^2\right]\psi(x,\lambda)=0$$
is described. It is shown that all the equations from this class are completely integrable hamiltonian systems; the corresponding “action-angle” variables are explicitly calculated. For $q=\varepsilon p^*$, $\varepsilon=\pm1$ this class contains such physically interesting equations as the modified nonlinear Schrödinger equation ($iq_t+q_{xx}-i\varepsilon(q^2q^*)_x=0$), the massive Thirring model and others.