Helminck, Gerard F.; Weenink, Jeffrey A. Homogeneous spaces yielding solutions of the \(k[S]\)-hierarchy and its strict version. (English) Zbl 1488.22013 Vestn. Ross. Univ., Mat. 26, No. 135, 315-336 (2021). MSC: 22E65 35Q53 37K10 58B25 PDFBibTeX XMLCite \textit{G. F. Helminck} and \textit{J. A. Weenink}, Vestn. Ross. Univ., Mat. 26, No. 135, 315--336 (2021; Zbl 1488.22013) Full Text: DOI MNR
Helminck, G. F.; Panasenko, E. A. Darboux transformations for the strict KP hierarchy. (English. Russian original) Zbl 1477.37079 Theor. Math. Phys. 206, No. 3, 296-314 (2021); translation from Teor. Mat. Fiz. 206, No. 3, 339-360 (2021). Reviewer: Giulio Landolfi (Lecce) MSC: 37K35 37K10 37K25 PDFBibTeX XMLCite \textit{G. F. Helminck} and \textit{E. A. Panasenko}, Theor. Math. Phys. 206, No. 3, 296--314 (2021; Zbl 1477.37079); translation from Teor. Mat. Fiz. 206, No. 3, 339--360 (2021) Full Text: DOI
Helminck, G. F.; Panasenko, E. A. Reductions of the strict KP hierarchy. (English. Russian original) Zbl 1456.37073 Theor. Math. Phys. 205, No. 2, 1411-1425 (2020); translation from Teor. Mat. Fiz. 205, No. 2, 190-207 (2020). MSC: 37K10 37K30 PDFBibTeX XMLCite \textit{G. F. Helminck} and \textit{E. A. Panasenko}, Theor. Math. Phys. 205, No. 2, 1411--1425 (2020; Zbl 1456.37073); translation from Teor. Mat. Fiz. 205, No. 2, 190--207 (2020) Full Text: DOI
Helminck, G. F.; Poberezhny, V. A.; Polenkova, S. V. Extensions of the discrete KP hierarchy and its strict version. (English. Russian original) Zbl 1470.37085 Theor. Math. Phys. 204, No. 3, 1140-1153 (2020); translation from Teor. Mat. Fiz. 204, No. 3, 367-382 (2020). Reviewer: Jipeng Cheng (Xuzhou) MSC: 37J70 37K10 39A36 PDFBibTeX XMLCite \textit{G. F. Helminck} et al., Theor. Math. Phys. 204, No. 3, 1140--1153 (2020; Zbl 1470.37085); translation from Teor. Mat. Fiz. 204, No. 3, 367--382 (2020) Full Text: DOI
Helminck, G. F.; Weenink, J. A. Integrable hierarchies in the \(\mathbb{N} \times \mathbb{N}\)-matrices related to powers of the shift operator. (English) Zbl 1436.37079 J. Geom. Phys. 148, Article ID 103560, 23 p. (2020). MSC: 37K10 37K25 37K30 PDFBibTeX XMLCite \textit{G. F. Helminck} and \textit{J. A. Weenink}, J. Geom. Phys. 148, Article ID 103560, 23 p. (2020; Zbl 1436.37079) Full Text: DOI
Helminck, G. F.; Panasenko, E. A. Expressions in Fredholm determinants for solutions of the strict KP hierarchy. (English. Russian original) Zbl 1429.37038 Theor. Math. Phys. 199, No. 2, 637-651 (2019); translation from Teor. Mat. Fiz. 199, No. 2, 193-209 (2019). MSC: 37K10 37K20 37K30 PDFBibTeX XMLCite \textit{G. F. Helminck} and \textit{E. A. Panasenko}, Theor. Math. Phys. 199, No. 2, 637--651 (2019; Zbl 1429.37038); translation from Teor. Mat. Fiz. 199, No. 2, 193--209 (2019) Full Text: DOI
Helminck, G. F. A geometric construction of solutions of the strict \(\mathbf{h}\)-hierarchy. (English. Russian original) Zbl 1429.37037 Theor. Math. Phys. 200, No. 1, 985-1005 (2019); translation from Teor. Mat. Fiz. 200, No. 1, 72-95 (2019). MSC: 37K10 37K25 37K30 PDFBibTeX XMLCite \textit{G. F. Helminck}, Theor. Math. Phys. 200, No. 1, 985--1005 (2019; Zbl 1429.37037); translation from Teor. Mat. Fiz. 200, No. 1, 72--95 (2019) Full Text: DOI
Helminck, G. F.; Panasenko, E. A. Geometric solutions of the strict KP hierarchy. (English. Russian original) Zbl 1416.37062 Theor. Math. Phys. 198, No. 1, 48-68 (2019); translation from Teor. Mat. Fiz. 198, No. 1, 54-78 (2019). MSC: 37K10 37K30 35Q53 37K20 PDFBibTeX XMLCite \textit{G. F. Helminck} and \textit{E. A. Panasenko}, Theor. Math. Phys. 198, No. 1, 48--68 (2019; Zbl 1416.37062); translation from Teor. Mat. Fiz. 198, No. 1, 54--78 (2019) Full Text: DOI
Helminck, G. F.; Poberezhny, V. A.; Polenkova, S. V. A geometric construction of solutions of the strict \(\mathrm{dKP}(\Lambda_0)\) hierarchy. (English) Zbl 1391.37049 J. Geom. Phys. 131, 189-203 (2018). MSC: 37K10 37K40 39A70 PDFBibTeX XMLCite \textit{G. F. Helminck} et al., J. Geom. Phys. 131, 189--203 (2018; Zbl 1391.37049) Full Text: DOI
Helminck, G. F. An integrable hierarchy including the AKNS hierarchy and its strict version. (English. Russian original) Zbl 1396.37069 Theor. Math. Phys. 192, No. 3, 1324-1336 (2017); translation from Teor. Mat. Fiz. 192, No. 3, 444-458 (2017). Reviewer: Johanna Michor (Wien) MSC: 37K10 37K30 PDFBibTeX XMLCite \textit{G. F. Helminck}, Theor. Math. Phys. 192, No. 3, 1324--1336 (2017; Zbl 1396.37069); translation from Teor. Mat. Fiz. 192, No. 3, 444--458 (2017) Full Text: DOI
Helminck, G. F. The strict AKNS hierarchy: its structure and solutions. (English) Zbl 1369.37073 Adv. Math. Phys. 2016, Article ID 3649205, 10 p. (2016). Reviewer: Chuanzhong Li (Ningbo) MSC: 37K10 37K25 37K30 22E67 PDFBibTeX XMLCite \textit{G. F. Helminck}, Adv. Math. Phys. 2016, Article ID 3649205, 10 p. (2016; Zbl 1369.37073) Full Text: DOI arXiv
Helminck, Gerard F.; van de Leur, Johan W. Geometric Bäcklund-Darboux transformations for the KP hierarchy. (English) Zbl 1028.37043 Publ. Res. Inst. Math. Sci. 37, No. 4, 479-519 (2001). Reviewer: C.Udrişte (Bucureşti) MSC: 37K35 35A22 37K10 35Q53 58B25 PDFBibTeX XMLCite \textit{G. F. Helminck} and \textit{J. W. van de Leur}, Publ. Res. Inst. Math. Sci. 37, No. 4, 479--519 (2001; Zbl 1028.37043) Full Text: DOI arXiv
Helminck, G. F.; van de Leur, J. W. Darboux transformations for the KP hierarchy in the Segal-Wilson setting. (English) Zbl 0970.22017 Can. J. Math. 53, No. 2, 278-309 (2001). Reviewer: Constantin Udrişte (Bucureşti) MSC: 22E65 22E70 35Q53 35Q58 58B25 PDFBibTeX XMLCite \textit{G. F. Helminck} and \textit{J. W. van de Leur}, Can. J. Math. 53, No. 2, 278--309 (2001; Zbl 0970.22017) Full Text: DOI
Helminck, G. F.; Helminck, A. G. Infinite-dimensional flag manifolds in integrable systems. (English) Zbl 0838.22008 Acta Appl. Math. 41, No. 1-3, 99-121 (1995). Reviewer: C.Udrişte (Bucureşti) MSC: 22E65 14M15 35Q58 43A80 17B65 PDFBibTeX XMLCite \textit{G. F. Helminck} and \textit{A. G. Helminck}, Acta Appl. Math. 41, No. 1--3, 99--121 (1995; Zbl 0838.22008) Full Text: DOI
Helminck, G. F.; Post, G. F. The geometry of differential difference equations. (English) Zbl 0816.35123 Indag. Math., New Ser. 5, No. 4, 411-438 (1994). MSC: 35Q53 37J35 37K10 35R10 PDFBibTeX XMLCite \textit{G. F. Helminck} and \textit{G. F. Post}, Indag. Math., New Ser. 5, No. 4, 411--438 (1994; Zbl 0816.35123) Full Text: DOI Link
Helminck, Gerard F.; Helminck, Aloysius G. The structure of Hilbert flag varieties. (English) Zbl 0836.22029 Publ. Res. Inst. Math. Sci. 30, No. 3, 401-441 (1994). Reviewer: N.I.Osetinski (Moskva) MSC: 22E65 14M15 35Q58 43A80 17B65 PDFBibTeX XMLCite \textit{G. F. Helminck} and \textit{A. G. Helminck}, Publ. Res. Inst. Math. Sci. 30, No. 3, 401--441 (1994; Zbl 0836.22029) Full Text: DOI
Helminck, G. F.; Post, G. F. Geometrical interpretation of the bilinear equations of the KP hierarchy. (English) Zbl 0672.58047 Lett. Math. Phys. 16, No. 4, 359-364 (1988). Reviewer: H.Yamada MSC: 58J99 37J35 37K10 35Q99 17B65 PDFBibTeX XMLCite \textit{G. F. Helminck} and \textit{G. F. Post}, Lett. Math. Phys. 16, No. 4, 359--364 (1988; Zbl 0672.58047) Full Text: DOI