Geodesic
Some thoughts on a~nonlinear Schr\"odinger equation motivated by
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 157-162

Voir la notice de l'article provenant de la source Math-Net.Ru

The arguments leading to a nonlinear generalization of the Schrödinger equation in the context of the maximum uncertainty principle are reviewed. The exact and perturbative properties of that equation depend on a free regulating/interpolating parameter $\eta$, which can be fixed using energetics as is shown here. A linear theory with an external potential that reproduces some unusual exact solutions of the nonlinear equation is also discussed, together with possible symmetry enhancements in the nonlinear theory.
Keywords: nonlinear Schrödinger equation, information theory, degeneration. 
@article{TMF_2007_152_1_a11,
     author = {R. R. Parwani},
     title = {Some thoughts on a~nonlinear {Schr\"odinger} equation motivated by},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {157--162},
     publisher = {mathdoc},
     volume = {152},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a11/}
}
TY  - JOUR
AU  - R. R. Parwani
TI  - Some thoughts on a~nonlinear Schr\"odinger equation motivated by
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2007
SP  - 157
EP  - 162
VL  - 152
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a11/
LA  - ru
ID  - TMF_2007_152_1_a11
ER  - 
%0 Journal Article
%A R. R. Parwani
%T Some thoughts on a~nonlinear Schr\"odinger equation motivated by
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2007
%P 157-162
%V 152
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a11/
%G ru
%F TMF_2007_152_1_a11
R. R. Parwani. Some thoughts on a~nonlinear Schr\"odinger equation motivated by. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 157-162. http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a11/