Geodesic
Extensions of the discrete KP hierarchy and its strict version
Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 3, pp. 367-382 Cet article a éte moissonné depuis la source Math-Net.Ru

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We show that both the dKP hierarchy and its strict version can be extended to a wider class of deformations satisfying a larger set of Lax equations. We prove that both extended hierarchies have appropriate linearizations allowing a geometric construction of their solutions.
Keywords: pseudodifference operator, hierarchy, linearization, oscillating matrix, geometric construction of solutions.
Mots-clés : wave matrix 
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G. F. Helminck; V. A. Poberezhny; S. V. Polenkova. Extensions of the discrete KP hierarchy and its strict version. Teoretičeskaâ i matematičeskaâ fizika, Tome 204 (2020) no. 3, pp. 367-382. http://geodesic.mathdoc.fr/item/TMF_2020_204_3_a3/

[1] M. Adler, P. van Moerbeke, “Vertex operator solutions to the discrete KP-hierarchy”, Commun. Math. Phys., 203:1 (1999), 185–210, arXiv: solv-int/9912014 | DOI | MR

[2] G. F. Khelmink, V. A. Poberezhnyi, S. V. Polenkova, “Strogie versii integriruemykh ierarkhii psevdoraznostnykh operatorov i soputstvuyuschikh zadach Koshi”, TMF, 198:2 (2019), 225–245 | DOI | DOI

[3] G. F. Helminck, V. A. Poberezhny, S. V. Polenkova, “A geometric construction of solutions of the strict $\text{dKP}(\Lambda_0$) hierarchy”, J. Geom. Phys., 131 (2018), 189–203 | DOI | MR

[4] G. Segal, G. Wilson, “Loop groups and equations of KdV type”, Publ. Math. Inst. Hautes Étud. Sci., 61 (1985), 5–65 | DOI | MR | Zbl

[5] G. F. Khelmink, E. A. Panasenko, “Geometricheskie resheniya strogoi ierarkhii Kadomtseva–Petviashvili”, TMF, 198:1 (2019), 54–78 | DOI | DOI

[6] E. Presli, G. Sigal, Gruppy petel, Mir, M., 1990 | MR