Geodesic
A hierarchy of generalized invariants for linear partial differential
Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 3, pp. 470-478 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We study invariants of linear partial differential operators in two variables under gauge transformations. Using the Beals–Kartashova factorization, we construct a hierarchy of generalized invariants for operators of an arbitrary order. We study the properties of these invariants and give some examples. We also show that the classic Laplace invariants correspond to some particular cases of generalized invariants.
Keywords: linear partial differential operator, Beals–Kartashova factorization, generalized invariant, hierarchy of invariants. 
@article{TMF_2006_147_3_a4,
     author = {E. A. Kartashova},
     title = {A hierarchy of generalized invariants for linear partial differential},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {470--478},
     year = {2006},
     volume = {147},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2006_147_3_a4/}
}
TY  - JOUR
AU  - E. A. Kartashova
TI  - A hierarchy of generalized invariants for linear partial differential
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2006
SP  - 470
EP  - 478
VL  - 147
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_2006_147_3_a4/
LA  - ru
ID  - TMF_2006_147_3_a4
ER  - 
%0 Journal Article
%A E. A. Kartashova
%T A hierarchy of generalized invariants for linear partial differential
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2006
%P 470-478
%V 147
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_2006_147_3_a4/
%G ru
%F TMF_2006_147_3_a4
E. A. Kartashova. A hierarchy of generalized invariants for linear partial differential. Teoretičeskaâ i matematičeskaâ fizika, Tome 147 (2006) no. 3, pp. 470-478. http://geodesic.mathdoc.fr/item/TMF_2006_147_3_a4/

[1] A. B. Shabat, TMF, 103:1 (1995), 170–175 | MR | Zbl

[2] L. Bianchi, Lezioni di Geometria Differenziale, Zanichelli, Bologna, 1924 ; А. Н. Лезнов, М. В. Савельев, Групповые методы интегрирования нелинейных динамических систем, Наука, М., 1985 ; S. P. Tsarev, “An algorithm for complete enumeration of all factorizations of a linear ordinary differential operator”, Proc. of the Int. Symp. on Symbolic and Algebraic Computation ISSAC' 96 (Zurich, Switzerland, July 24–26, 1996), ed. Y. N. Lakshman, ACM Press, N.Y., 1996, 226–231 ; S. P. Tsarev, “Factorization of linear partial differential operators and Darboux integrability of nonlinear PDEs”, Poster at ISSAC' 98 (Rostock, Germany, August 13–15, 1998), 1998 ; ; G. Tzitzeica, Compt. Rend. Acad. Sci., 150 (1910), 955–956; 971–974 cs.SC/9811002 | Zbl | MR | Zbl | Zbl | Zbl | Zbl

[3] D. Grigoriev, F. Schwarz, J. Comput., 73 (2004), 179–197 | MR | Zbl

[4] E. Kaltofen, “Factorization of polynomials”, Computing (Archive vor Informatics and Numerical Computation), eds. B. Buchberger, G. E. Collins and R. Loos, Springer, Wien, 1982, 95–113 | MR

[5] R. Bils, E. A. Kartashova, TMF, 145 (2005), 165–180 | DOI | MR

[6] E. Kartashova, “BK-factorization and Darboux–Laplace transformations”, Int. Conf. on Scientific Computing, Proc. CSC' 05 (Las Vegas, Nevada, USA, June 20–23, 2005), eds. H. R. Arabnia, G. A. Gravvanis, C.S.R.E.A. Press, Athens, Georgia, USA, 2005, 144–150