Geodesic
Quadratic bundle and nonlinear equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 44 (1980) no. 3, pp. 342-357 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {Quadratic bundle and nonlinear equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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V. S. Gerdjikov; M. I. Ivanov; P. P. Kulish. Quadratic bundle and nonlinear equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 44 (1980) no. 3, pp. 342-357. http://geodesic.mathdoc.fr/item/TMF_1980_44_3_a4/

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