Geodesic
Investigation of the exact integrability of the multiwave Schr\"odinger equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 2, pp. 242-253

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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. 
@article{TMF_1997_110_2_a4,
     author = {S. V. Belyutin},
     title = {Investigation of the exact integrability of the multiwave {Schr\"odinger} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {242--253},
     publisher = {mathdoc},
     volume = {110},
     number = {2},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1997_110_2_a4/}
}
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S. V. Belyutin. Investigation of the exact integrability of the multiwave Schr\"odinger equation. Teoretičeskaâ i matematičeskaâ fizika, Tome 110 (1997) no. 2, pp. 242-253. http://geodesic.mathdoc.fr/item/TMF_1997_110_2_a4/