Geodesic
Investigation of the exact integrability of the multiwave Schrödinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 2, pp. 242-253 
S. V. Belyutin. Investigation of the exact integrability of the multiwave Schrödinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 2, pp. 242-253. http://geodesic.mathdoc.fr/item/TMF_1997_110_2_a4/
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     title = {Investigation of the exact integrability of the multiwave {Schr\"odinger} equation},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_110_2_a4/}
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It is shown that the multiwave nonlinear Schrödinger equation, which describes evolution of several quasi-monochromatic waves with equal group velocities, is not exactly integrable: it does not have infinite sequence of local conservation laws and symmetries. Exact integrability of the system of equations $w_t^i=\alpha_iw_{xx}^i+a_{klm}^iw^kw^lw^m$ with the nondegenerate diagonal matrix at the second-order derivative is studied.

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