Nonlinear Schr\"odinger equation with noncompact isogroup
Teoretičeskaâ i matematičeskaâ fizika, Tome 53 (1982) no. 1, pp. 55-67
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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.
@article{TMF_1982_53_1_a5,
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},
publisher = {mathdoc},
volume = {53},
number = {1},
year = {1982},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1982_53_1_a5/}
}
TY - JOUR AU - V. G. Makhan'kov AU - O. K. Pashaev TI - Nonlinear Schr\"odinger equation with noncompact isogroup JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1982 SP - 55 EP - 67 VL - 53 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1982_53_1_a5/ LA - ru ID - TMF_1982_53_1_a5 ER -
V. G. Makhan'kov; O. K. Pashaev. Nonlinear Schr\"odinger 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/