Dubrovin, Boris; Yang, Di; Zagier, Don Geometry and arithmetic of integrable hierarchies of KdV type. I: Integrality. (English) Zbl 1524.14075 Adv. Math. 433, Article ID 109311, 73 p. (2023). Reviewer: Ahmed Lesfari (El Jadida) MSC: 14H70 14H10 37K10 37K20 53D45 53D50 PDFBibTeX XMLCite \textit{B. Dubrovin} et al., Adv. Math. 433, Article ID 109311, 73 p. (2023; Zbl 1524.14075) Full Text: DOI arXiv
Dubrovin, Boris; Valeri, Daniele; Yang, Di Affine Kac-Moody algebras and tau-functions for the Drinfeld-Sokolov hierarchies: the matrix-resolvent method. (English) Zbl 1508.37088 SIGMA, Symmetry Integrability Geom. Methods Appl. 18, Paper 077, 32 p. (2022). Reviewer: Ma Wen-Xiu (Tampa) MSC: 37K10 37K30 35Q51 17B80 17B67 PDFBibTeX XMLCite \textit{B. Dubrovin} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 18, Paper 077, 32 p. (2022; Zbl 1508.37088) Full Text: DOI arXiv
Bertola, Marco; Dubrovin, Boris; Yang, Di Simple Lie algebras, Drinfeld-Sokolov hierarchies, and multi-point correlation functions. (English) Zbl 1482.37066 Mosc. Math. J. 21, No. 2, 233-270 (2021). Reviewer: Ahmed Lesfari (El Jadida) MSC: 37K10 37K25 37K20 37K30 17B80 14N35 PDFBibTeX XMLCite \textit{M. Bertola} et al., Mosc. Math. J. 21, No. 2, 233--270 (2021; Zbl 1482.37066) Full Text: arXiv Link
Dubrovin, Boris; Yang, Di; Zagier, Don On tau-functions for the KdV hierarchy. (English) Zbl 1458.14061 Sel. Math., New Ser. 27, No. 1, Paper No. 12, 48 p. (2021). Reviewer: Ahmed Lesfari (El Jadida) MSC: 14N35 37K10 53D45 05A15 33E15 PDFBibTeX XMLCite \textit{B. Dubrovin} et al., Sel. Math., New Ser. 27, No. 1, Paper No. 12, 48 p. (2021; Zbl 1458.14061) Full Text: DOI arXiv Link
Dubrovin, Boris; Liu, Si-Qi; Yang, Di; Zhang, Youjin Hodge-GUE correspondence and the discrete KdV equation. (English) Zbl 1455.37056 Commun. Math. Phys. 379, No. 2, 461-490 (2020). Reviewer: Jipeng Cheng (Xuzhou) MSC: 37K20 37K60 37K25 37K10 39A36 58A14 PDFBibTeX XMLCite \textit{B. Dubrovin} et al., Commun. Math. Phys. 379, No. 2, 461--490 (2020; Zbl 1455.37056) Full Text: DOI arXiv
Dubrovin, Boris; Yang, Di Matrix resolvent and the discrete KdV hierarchy. (English) Zbl 1454.37065 Commun. Math. Phys. 377, No. 3, 1823-1852 (2020). Reviewer: Dmitry Pelinovsky (Hamilton) MSC: 37K10 37K20 37K25 37K60 PDFBibTeX XMLCite \textit{B. Dubrovin} and \textit{D. Yang}, Commun. Math. Phys. 377, No. 3, 1823--1852 (2020; Zbl 1454.37065) Full Text: DOI arXiv
Cotti, Giordano; Dubrovin, Boris; Guzzetti, Davide Local moduli of semisimple Frobenius coalescent structures. (English) Zbl 1442.53060 SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 040, 105 p. (2020). MSC: 53D45 34M56 18G80 PDFBibTeX XMLCite \textit{G. Cotti} et al., SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 040, 105 p. (2020; Zbl 1442.53060) Full Text: DOI arXiv
Dubrovin, B.; Skrypnyk, T. Separation of variables for quadratic algebras and skew-symmetric classical \(r\)-matrices. (English) Zbl 1436.70005 J. Math. Phys. 60, No. 9, 093506, 30 p. (2019). MSC: 70H06 37K10 17B80 PDFBibTeX XMLCite \textit{B. Dubrovin} and \textit{T. Skrypnyk}, J. Math. Phys. 60, No. 9, 093506, 30 p. (2019; Zbl 1436.70005) Full Text: DOI
Dubrovin, Boris; Strachan, Ian A. B.; Zhang, Youjin; Zuo, Dafeng Extended affine Weyl groups of BCD-type: their Frobenius manifolds and Landau-Ginzburg superpotentials. (English) Zbl 1418.53088 Adv. Math. 351, 897-946 (2019). MSC: 53D45 PDFBibTeX XMLCite \textit{B. Dubrovin} et al., Adv. Math. 351, 897--946 (2019; Zbl 1418.53088) Full Text: DOI arXiv
Buryak, Alexandr; Dubrovin, Boris; Guéré, Jérémy; Rossi, Paolo Tau-structure for the double ramification hierarchies. (English) Zbl 1431.53095 Commun. Math. Phys. 363, No. 1, 191-260 (2018). MSC: 53D45 14N35 37K10 PDFBibTeX XMLCite \textit{A. Buryak} et al., Commun. Math. Phys. 363, No. 1, 191--260 (2018; Zbl 1431.53095) Full Text: DOI arXiv Link
Dubrovin, Boris; Kapaev, Andrei A Riemann-Hilbert approach to the Heun equation. (English) Zbl 1404.34100 SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 093, 24 p. (2018). Reviewer: Pascal Remy (Carrières-sur-Seine) MSC: 34M03 34M05 34M35 34M55 57M50 PDFBibTeX XMLCite \textit{B. Dubrovin} and \textit{A. Kapaev}, SIGMA, Symmetry Integrability Geom. Methods Appl. 14, Paper 093, 24 p. (2018; Zbl 1404.34100) Full Text: DOI arXiv
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin Bihamiltonian cohomologies and integrable hierarchies. II: The tau structures. (English) Zbl 1403.37072 Commun. Math. Phys. 361, No. 2, 467-524 (2018). Reviewer: Tihomir Valchev (Sofia) MSC: 37K05 37K10 37K20 37K25 PDFBibTeX XMLCite \textit{B. Dubrovin} et al., Commun. Math. Phys. 361, No. 2, 467--524 (2018; Zbl 1403.37072) Full Text: DOI arXiv
Dubrovin, Boris; Yang, Di Generating series for GUE correlators. (English) Zbl 1380.37126 Lett. Math. Phys. 107, No. 11, 1971-2012 (2017). Reviewer: Ma Wen-Xiu (Tampa) MSC: 37K10 37K20 PDFBibTeX XMLCite \textit{B. Dubrovin} and \textit{D. Yang}, Lett. Math. Phys. 107, No. 11, 1971--2012 (2017; Zbl 1380.37126) Full Text: DOI arXiv
Dubrovin, B.; Grava, T.; Klein, C. On critical behaviour in generalized Kadomtsev-Petviashvili equations. (English) Zbl 1415.37095 Physica D 333, 157-170 (2016). MSC: 37K40 35Q51 35B44 PDFBibTeX XMLCite \textit{B. Dubrovin} et al., Physica D 333, 157--170 (2016; Zbl 1415.37095) Full Text: DOI arXiv
Bertola, Marco; Dubrovin, Boris; Yang, Di Correlation functions of the KdV hierarchy and applications to intersection numbers over \(\overline{\mathcal{M}}_{g, n}\). (English) Zbl 1373.37153 Physica D 327, 30-57 (2016). MSC: 37K10 37K20 PDFBibTeX XMLCite \textit{M. Bertola} et al., Physica D 327, 30--57 (2016; Zbl 1373.37153) Full Text: DOI arXiv
Dubrovin, Boris; Liu, Si-Qi; Yang, Di; Zhang, Youjin Hodge integrals and tau-symmetric integrable hierarchies of Hamiltonian evolutionary PDEs. (English) Zbl 1335.53114 Adv. Math. 293, 382-435 (2016). MSC: 53D45 37K10 PDFBibTeX XMLCite \textit{B. Dubrovin} et al., Adv. Math. 293, 382--435 (2016; Zbl 1335.53114) Full Text: DOI arXiv
Dubrovin, Boris; Grava, Tamara; Klein, Christian; Moro, Antonio On critical behaviour in systems of Hamiltonian partial differential equations. (English) Zbl 1321.35208 J. Nonlinear Sci. 25, No. 3, 631-707 (2015). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q55 37K05 34M55 PDFBibTeX XMLCite \textit{B. Dubrovin} et al., J. Nonlinear Sci. 25, No. 3, 631--707 (2015; Zbl 1321.35208) Full Text: DOI arXiv
Belavin, Alexander; Dubrovin, Boris; Mukhametzhanov, Baur Minimal Liouville gravity correlation numbers from Douglas string equation. (English) Zbl 1333.83172 J. High Energy Phys. 2014, No. 1, Paper No. 156, 50 p. (2014). MSC: 83E30 PDFBibTeX XMLCite \textit{A. Belavin} et al., J. High Energy Phys. 2014, No. 1, Paper No. 156, 50 p. (2014; Zbl 1333.83172) Full Text: DOI arXiv
Dubrovin, B.; Kapaev, A. On an isomonodromy deformation equation without the Painlevé property. (English) Zbl 1322.34102 Russ. J. Math. Phys. 21, No. 1, 9-35 (2014). Reviewer: Tsvetana Stoyanova (Sofia) MSC: 34M56 34M35 34M40 34M50 PDFBibTeX XMLCite \textit{B. Dubrovin} and \textit{A. Kapaev}, Russ. J. Math. Phys. 21, No. 1, 9--35 (2014; Zbl 1322.34102) Full Text: DOI arXiv
Dubrovin, Boris (ed.); Hertling, Claus (ed.); Strachan, Ian A. B. (ed.); Wendland, Katrin (ed.) Singularity theory and integrable systems. Abstracts from the workshop held April 22–28, 2012. (English) Zbl 1349.00148 Oberwolfach Rep. 9, No. 2, 1361-1403 (2012). MSC: 00B05 00B25 14-06 32-06 58-06 14B05 32Sxx 37Kxx 58K99 PDFBibTeX XMLCite \textit{B. Dubrovin} (ed.) et al., Oberwolfach Rep. 9, No. 2, 1361--1403 (2012; Zbl 1349.00148) Full Text: DOI
Dubrovin, B.; Elaeva, M. On the critical behavior in nonlinear evolutionary PDEs with small viscosity. (English) Zbl 1263.35019 Russ. J. Math. Phys. 19, No. 4, 449-460 (2012). MSC: 35B25 PDFBibTeX XMLCite \textit{B. Dubrovin} and \textit{M. Elaeva}, Russ. J. Math. Phys. 19, No. 4, 449--460 (2012; Zbl 1263.35019) Full Text: DOI arXiv
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin On the genus two free energies for semisimple Frobenius manifolds. (English) Zbl 1325.53114 Russ. J. Math. Phys. 19, No. 3, 273-298 (2012). Reviewer: Xiaowen Hu (Beijing) MSC: 53D45 14N35 PDFBibTeX XMLCite \textit{B. Dubrovin} et al., Russ. J. Math. Phys. 19, No. 3, 273--298 (2012; Zbl 1325.53114) Full Text: DOI arXiv
Dubrovin, B. A.; Pavlov, M. V.; Zykov, S. A. Linearly degenerate Hamiltonian PDEs and a new class of solutions to the WDVV associativity equations. (English. Russian original) Zbl 1271.37044 Funct. Anal. Appl. 45, No. 4, 278-290 (2011); translation from Funkts. Anal. Prilozh. 45, No. 4, 49-64 (2011). MSC: 37K10 PDFBibTeX XMLCite \textit{B. A. Dubrovin} et al., Funct. Anal. Appl. 45, No. 4, 278--290 (2011; Zbl 1271.37044); translation from Funkts. Anal. Prilozh. 45, No. 4, 49--64 (2011) Full Text: DOI arXiv
Carlet, Guido; Dubrovin, Boris; Mertens, Luca Philippe Infinite-dimensional Frobenius manifolds for \(2+1\) integrable systems. (English) Zbl 1208.53090 Math. Ann. 349, No. 1, 75-115 (2011). Reviewer: Vehbi Emrah Paksoy (Fort Lauderdale) MSC: 53D45 35Q55 PDFBibTeX XMLCite \textit{G. Carlet} et al., Math. Ann. 349, No. 1, 75--115 (2011; Zbl 1208.53090) Full Text: DOI arXiv
Dubrovin, B.; Grava, T.; Klein, C. On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the Painlevé-I equation. (English) Zbl 1220.37048 J. Nonlinear Sci. 19, No. 1, 57-94 (2009). Reviewer: Bixiang Wang (Socorro) MSC: 37K05 35Q55 PDFBibTeX XMLCite \textit{B. Dubrovin} et al., J. Nonlinear Sci. 19, No. 1, 57--94 (2009; Zbl 1220.37048) Full Text: DOI arXiv
Dubrovin, Boris; Liu, Si-Qi; Zhang, Youjin Frobenius manifolds and central invariants for the Drinfeld-Sokolov bihamiltonian structures. (English) Zbl 1153.37032 Adv. Math. 219, No. 3, 780-837 (2008). Reviewer: Dimitar A. Kolev (Sofia) MSC: 37K10 PDFBibTeX XMLCite \textit{B. Dubrovin} et al., Adv. Math. 219, No. 3, 780--837 (2008; Zbl 1153.37032) Full Text: DOI arXiv
Dubrovin, Boris; Mazzocco, Marta Canonical structure and symmetries of the Schlesinger equations. (English) Zbl 1146.32005 Commun. Math. Phys. 271, No. 2, 289-373 (2007). Reviewer: Valentina Golubeva (Moskva) MSC: 32G34 14H70 34M50 34M55 37J35 37K20 PDFBibTeX XMLCite \textit{B. Dubrovin} and \textit{M. Mazzocco}, Commun. Math. Phys. 271, No. 2, 289--373 (2007; Zbl 1146.32005) Full Text: DOI arXiv
Dubrovin, Boris On Hamiltonian perturbations of hyperbolic systems of conservation laws. II: Universality of critical behaviour. (English) Zbl 1109.35070 Commun. Math. Phys. 267, No. 1, 117-139 (2006). MSC: 35L65 37K10 PDFBibTeX XMLCite \textit{B. Dubrovin}, Commun. Math. Phys. 267, No. 1, 117--139 (2006; Zbl 1109.35070) Full Text: DOI arXiv
Dubrovin, Boris; Zhang, Youjin Virasoro symmetries of the extended Toda hierarchy. (English) Zbl 1071.37054 Commun. Math. Phys. 250, No. 1, 161-193 (2004). Reviewer: Jan Chrastina (Brno) MSC: 37K60 37K05 17B68 37K10 PDFBibTeX XMLCite \textit{B. Dubrovin} and \textit{Y. Zhang}, Commun. Math. Phys. 250, No. 1, 161--193 (2004; Zbl 1071.37054) Full Text: DOI arXiv
Dubrovin, B. A.; Fokas, A. S.; Santini, P. M. Integrable functional equations and algebraic geometry. (English) Zbl 0815.39008 Duke Math. J. 76, No. 2, 645-668 (1994). Reviewer: J.Aczél (Waterloo/Ontario) MSC: 39B22 14J25 47N20 70F10 PDFBibTeX XMLCite \textit{B. A. Dubrovin} et al., Duke Math. J. 76, No. 2, 645--668 (1994; Zbl 0815.39008) Full Text: DOI
Dubrovin, B. Geometry and integrability of topological-antitopological fusion. (English) Zbl 0771.53042 Commun. Math. Phys. 152, No. 3, 539-564 (1993). Reviewer: A.O.Barut (Boulder) MSC: 53Z05 81T40 PDFBibTeX XMLCite \textit{B. Dubrovin}, Commun. Math. Phys. 152, No. 3, 539--564 (1993; Zbl 0771.53042) Full Text: DOI arXiv
Dubrovin, B. A. Hamiltonian formalism of Whitham-type hierarchies and topological Landau- Ginsburg models. (English) Zbl 0753.58039 Commun. Math. Phys. 145, No. 1, 195-207 (1992). Reviewer: Yu.E.Gliklikh (Voronezh) MSC: 58Z05 35Q53 58D25 37J99 PDFBibTeX XMLCite \textit{B. A. Dubrovin}, Commun. Math. Phys. 145, No. 1, 195--207 (1992; Zbl 0753.58039) Full Text: DOI
Dubrovin, B. A. Differential geometry of strongly integrable systems of hydrodynamic type. (English. Russian original) Zbl 0850.76008 Funct. Anal. Appl. 24, No. 4, 280-285 (1990); translation from Funkts. Anal. Prilozh. 24, No. 4, 25-30 (1990). MSC: 76-XX 37J35 37K10 PDFBibTeX XMLCite \textit{B. A. Dubrovin}, Funct. Anal. Appl. 24, No. 4, 280--285 (1990; Zbl 0850.76008); translation from Funkts. Anal. Prilozh. 24, No. 4, 25--30 (1990) Full Text: DOI
Dubrovin, B. Weakly deformed soliton lattices. (English) Zbl 1051.37502 Nucl. Phys., B, Proc. Suppl. 18A, 23-44 (1990). MSC: 37K10 35Q51 35Q58 PDFBibTeX XMLCite \textit{B. Dubrovin}, Nucl. Phys., B, Proc. Suppl. 18A, 23--44 (1990; Zbl 1051.37502) Full Text: DOI
Dubrovin, B. A. Matrix finite-zone operators. (English. Russian original) Zbl 0561.58043 J. Sov. Math. 28, 20-50 (1985); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 23, 33-78 (1983). Reviewer: N.Jacob MSC: 58J50 35P05 81Q99 PDFBibTeX XMLCite \textit{B. A. Dubrovin}, J. Sov. Math. 28, 20--50 (1985; Zbl 0561.58043); translation from Itogi Nauki Tekh., Ser. Sovrem. Probl. Mat. 23, 33--78 (1983) Full Text: DOI
Dubrovin, B. A.; Natanzon, S. M. Real two-zone solutions of the sine-Gordon equation. (Russian. English original) Zbl 0554.35100 Funct. Anal. Appl. 16, 21-33 (1982); translation from Funkts. Anal. Prilozh. 16, No. 1, 27-43 (1982). Reviewer: A.M.Šermenev MSC: 35Q99 30F99 PDFBibTeX XMLCite \textit{B. A. Dubrovin} and \textit{S. M. Natanzon}, Funct. Anal. Appl. 16, 21--33 (1982; Zbl 0554.35100); translation from Funkts. Anal. Prilozh. 16, No. 1, 27--43 (1982) Full Text: DOI
Dubrovin, B. A. Completely integrable Hamiltonian systems associated with matrix operators and abelian varieties. (English) Zbl 0413.58012 Funct. Anal. Appl. 11, 265-277 (1978). MSC: 37J99 PDFBibTeX XMLCite \textit{B. A. Dubrovin}, Funct. Anal. Appl. 11, 265--277 (1978; Zbl 0413.58012) Full Text: DOI
Dubrovin, B. A. Periodic problems for the Korteweg-de Vries equation in the class of finite band potentials. (English) Zbl 0358.35022 Funct. Anal. Appl. 9(1975), 215-223 (1976). MSC: 35G20 PDFBibTeX XMLCite \textit{B. A. Dubrovin}, Funct. Anal. Appl. 9, 215--223 (1976; Zbl 0358.35022) Full Text: DOI