Geodesic
Nonlinear Schrödinger equation with noncompact isogroup
Teoretičeskaâ i matematičeskaâ fizika, Tome 53 (1982) no. 1, pp. 55-67 
V. G. Makhan'kov; O. K. Pashaev. Nonlinear Schrödinger equation with noncompact isogroup. Teoretičeskaâ i matematičeskaâ fizika, Tome 53 (1982) no. 1, pp. 55-67. http://geodesic.mathdoc.fr/item/TMF_1982_53_1_a5/
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     author = {V. G. Makhan'kov and O. K. Pashaev},
     title = {Nonlinear {Schr\"odinger} equation with noncompact isogroup},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {55--67},
     year = {1982},
     volume = {53},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1982_53_1_a5/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The properties of the nonlinear Schrödinger equation with noncompact isogroup are investigated. The example of the $U(1,1)$ nonlinear Schrödinger equation reveals the significant differences between this system and the previously considered vector nonlinear Schrödinger equation. The main feature – the large set of admissible boundary conditions on the field functions – leads to a rich spectrum of solutions of the system. Four types of boundary conditions and the corresponding soliton solutions are considered for the $U(1,1)$ model. Quasiclassical quantization of the solitons admits an interpretation in the language of “drops” and “bubbles” as bound states of a large number of bosons of the basic fields subject to the thermodynamic relations for a mixture of gases. The system is a continuous “analog” of the Hubbard model for zero-value boundary conditions, and therefore the paper ends with a discussion of this case.

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