Geodesic
Model equation of the~theory of solitons
Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 29-45

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

We consider the hierarchy of integrable $(1+2)$-dimensional equations related to the Lie algebra of vector fields on the line. We construct solutions in quadratures that contain $n$ arbitrary functions of a single argument. A simple equation for the generating function of the hierarchy, which determines the dynamics in negative times and finds applications to second-order spectral problems, is of main interest. Considering its polynomial solutions under the condition that the corresponding potential is regular allows developing a rather general theory of integrable $(1+1)$-dimensional equations.
Keywords: hierarchy of commuting vector fields
Mots-clés : Riemann invariant, Dubrovin equations. 
@article{TMF_2007_153_1_a2,
     author = {V. E. Adler and A. B. Shabat},
     title = {Model equation of the~theory of solitons},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {29--45},
     publisher = {mathdoc},
     volume = {153},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a2/}
}
TY  - JOUR
AU  - V. E. Adler
AU  - A. B. Shabat
TI  - Model equation of the~theory of solitons
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2007
SP  - 29
EP  - 45
VL  - 153
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a2/
LA  - ru
ID  - TMF_2007_153_1_a2
ER  - 
%0 Journal Article
%A V. E. Adler
%A A. B. Shabat
%T Model equation of the~theory of solitons
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2007
%P 29-45
%V 153
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a2/
%G ru
%F TMF_2007_153_1_a2
V. E. Adler; A. B. Shabat. Model equation of the~theory of solitons. Teoretičeskaâ i matematičeskaâ fizika, Tome 153 (2007) no. 1, pp. 29-45. http://geodesic.mathdoc.fr/item/TMF_2007_153_1_a2/