Geodesic
Some exact solutions of a~system of nonlinear Schr\"odinger equations in three-dimensional space
Teoretičeskaâ i matematičeskaâ fizika, Tome 72 (1987) no. 2, pp. 172-182

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Most general interaction terms are constructed which reduce the symmetry group of the nonrelativistic Schrödinger equations to its one-parameter subgroups. Ansatze of invariant solutions of the Galilei-invariant Schrödinger equations and corresponding systems of reduced equations in terms of invariant variables are found. Some exact solutions of the system of nonlinear Schrödinger equations are obtained in three spatial dimensions for the case of the generalised Hubbard model. 
@article{TMF_1987_72_2_a1,
     author = {S. S. Moskalyuk},
     title = {Some exact solutions of a~system of nonlinear {Schr\"odinger} equations in three-dimensional space},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {172--182},
     publisher = {mathdoc},
     volume = {72},
     number = {2},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1987_72_2_a1/}
}
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S. S. Moskalyuk. Some exact solutions of a~system of nonlinear Schr\"odinger equations in three-dimensional space. Teoretičeskaâ i matematičeskaâ fizika, Tome 72 (1987) no. 2, pp. 172-182. http://geodesic.mathdoc.fr/item/TMF_1987_72_2_a1/