Saunders, David Lepage equivalents and the variational bicomplex. (English) Zbl 1535.58003 SIGMA, Symmetry Integrability Geom. Methods Appl. 20, Paper 013, 18 p. (2024). Reviewer: Savin Treanţă (Bucureşti) MSC: 58A10 58A20 83D05 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Laurent, Adrien The Lie derivative and Noether’s theorem on the aromatic bicomplex for the study of volume-preserving numerical integrators. (English) Zbl 1542.37067 J. Comput. Dyn. 11, No. 1, 10-22 (2024). MSC: 37M15 65L06 58A12 58J10 05C90 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Laurent, Adrien; McLachlan, Robert I.; Munthe-Kaas, Hans Z.; Verdier, Olivier The aromatic bicomplex for the description of divergence-free aromatic forms and volume-preserving integrators. (English) Zbl 1527.37090 Forum Math. Sigma 11, Paper No. e69, 39 p. (2023). Reviewer: Kevin Burrage (Brisbane) MSC: 37M15 41A58 05C05 65L06 58A12 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Olver, Peter J. Divergence invariant variational problems. (English) Zbl 1516.70019 Read, James (ed.) et al., The philosophy and physics of Noether’s theorems. A centenary volume. Cambridge: Cambridge University Press. 134-143 (2022). MSC: 70G75 70G65 70H33 × Cite Format Result Cite Review PDF Full Text: DOI Link
Fels, M. E.; Yaşar, E. Variational operators, symplectic operators, and the cohomology of scalar evolution equations. (English) Zbl 1418.58006 J. Nonlinear Math. Phys. 26, No. 4, 604-649 (2019). MSC: 58E30 58A20 37K05 37K10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hashimoto, Kaname; Kato, Shin Bicomplex extensions of zero mean curvature surfaces in \(\mathbb{R}^{2, 1}\) and \(\mathbb{R}^{2, 2}\). (English) Zbl 1414.53052 J. Geom. Phys. 138, 223-240 (2019). MSC: 53C42 58E12 × Cite Format Result Cite Review PDF Full Text: DOI
Sharapov, A. A. BRST theory in the formalism of variational tricomplex. (English. Russian original) Zbl 1385.81042 Russ. Phys. J. 59, No. 11, 1911-1920 (2017); translation from Izv. Vyssh. Uchebn. Zaved., Fiz. 59, No. 11, 157-164 (2016). MSC: 81T70 81T13 81S10 × Cite Format Result Cite Review PDF Full Text: DOI
Zharinov, V. V. Lie-Poisson structures over differential algebras. (English. Russian original) Zbl 1383.37057 Theor. Math. Phys. 192, No. 3, 1337-1349 (2017); translation from Teor. Mat. Fiz. 192, No. 3, 459-472 (2017). Reviewer: Ahmed Lesfari (El Jadida) MSC: 37K05 37K25 12H05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sharapov, Alexey A. Variational tricomplex, global symmetries and conservation laws of gauge systems. (English) Zbl 1354.70059 SIGMA, Symmetry Integrability Geom. Methods Appl. 12, Paper 098, 24 p. (2016). MSC: 70S10 81T70 83C40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sardanashvily, Gennadi Noether’s theorems. Applications in mechanics and field theory. (English) Zbl 1357.58002 Atlantis Studies in Variational Geometry 3. Amsterdam: Atlantis Press (ISBN 978-94-6239-170-3/hbk; 978-94-6239-171-0/ebook). xvii, 297 p. (2016). Reviewer: Miguel Paternain (Montevideo) MSC: 58-02 58J90 58Z05 70-02 49Q20 58A50 70S05 58E15 × Cite Format Result Cite Review PDF Full Text: DOI
Benson, Joe Integrable equations and recursion operators in planar Klein geometries. (English) Zbl 1360.37163 Lobachevskii J. Math. 36, No. 3, 234-244 (2015). MSC: 37K10 53C44 58D25 35A30 35Q51 × Cite Format Result Cite Review PDF Full Text: DOI
Krupka, Demeter; Moreno, Giovanni; Urban, Zbyněk; Volná, Jana On a bicomplex induced by the variational sequence. (English) Zbl 1322.58013 Int. J. Geom. Methods Mod. Phys. 12, No. 5, Article ID 1550057, 15 p. (2015). Reviewer: Mohsen Timoumi (Monastir) MSC: 58E30 58A10 58A20 70G75 × Cite Format Result Cite Review PDF Full Text: DOI
Khavkine, Igor Presymplectic current and the inverse problem of the calculus of variations. (English) Zbl 1290.35330 J. Math. Phys. 54, No. 11, 111502, 11 p. (2013). MSC: 35R30 35A15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Sardanashvily, G. Graded Lagrangian formalism. (English) Zbl 1387.70030 Int. J. Geom. Methods Mod. Phys. 10, No. 5, Article ID 1350016, 37 p. (2013). MSC: 70S05 58A20 58A50 × Cite Format Result Cite Review PDF Full Text: DOI
Preston, Serge Balance systems and the variational bicomplex. (English) Zbl 1244.49076 SIGMA, Symmetry Integrability Geom. Methods Appl. 7, Paper 063, 18 p. (2011). MSC: 49S05 49M27 35Q79 74A15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Thompson, Robert; Valiquette, Francis On the cohomology of the invariant Euler–Lagrange complex. (English) Zbl 1251.49048 Acta Appl. Math. 116, No. 2, 199-226 (2011). MSC: 49N45 58E30 58H05 × Cite Format Result Cite Review PDF Full Text: DOI
Olver, Peter J. Lectures on moving frames. (English) Zbl 1235.53016 Levi, Decio (ed.) et al., Symmetries and integrability of difference equations. Based upon lectures delivered during the summer school, Montreal, Canada, June 8–21, 2008. Cambridge: Cambridge University Press (ISBN 978-0-521-13658-7/pbk). London Mathematical Society Lecture Note Series 381, 207-246 (2011). Reviewer: Benjamin McKay (Cork) MSC: 53A55 58J70 58A20 × Cite Format Result Cite Review PDF
Marí Beffa, G.; Olver, P. J. Poisson structures for geometric curve flows in semi-simple homogeneous spaces. (English) Zbl 1229.22018 Regul. Chaotic Dyn. 15, No. 4-5, 532-550 (2010). Reviewer: Ion Mihai (Bucureşti) MSC: 22F05 53D17 35A30 35Q53 53A55 58A20 × Cite Format Result Cite Review PDF Full Text: DOI
Saunders, D. J.; Crampin, M. The fundamental form of a homogeneous Lagrangian in two independent variables. (English) Zbl 1207.58016 J. Geom. Phys. 60, No. 11, 1681-1697 (2010). Reviewer: Vladislav Nikolaevich Dumachev (Voronezh) MSC: 58E15 58A15 57R17 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Crampin, M.; Saunders, D. J. Homotopy operators for the variational bicomplex, representations of the Euler-Lagrange complex, and the Helmholtz-Sonin conditions. (English) Zbl 1177.49056 Lobachevskii J. Math. 30, No. 2, 107-123 (2009). MSC: 49N45 58A20 58E30 × Cite Format Result Cite Review PDF Full Text: DOI
Saunders, D. J. Homogeneous variational complexes and bicomplexes. (English) Zbl 1168.58006 J. Geom. Phys. 59, No. 6, 727-739 (2009). Reviewer: Vladimir Balan (Bucureşti) MSC: 58E99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mikulski, W. M. Uniqueness results for operators in the variational sequence. (English) Zbl 1165.49041 Ann. Pol. Math. 95, No. 2, 125-133 (2009). MSC: 49Q99 49S05 58A20 58A32 × Cite Format Result Cite Review PDF Full Text: DOI
Pérez, Roberto Ferreiro Local cohomology and the variational bicomplex. (English) Zbl 1146.58004 Int. J. Geom. Methods Mod. Phys. 5, No. 4, 587-604 (2008). Reviewer: Miroslav Doupovec (Brno) MSC: 58A20 55N99 57R32 58D17 58E99 × Cite Format Result Cite Review PDF Full Text: DOI
Olver, Peter J.; Pohjanpelto, Juha Pseudo-groups, moving frames, and differential invariants. (English) Zbl 1144.58013 Eastwood, Michael (ed.) et al., Symmetries and overdetermined systems of partial differential equations. Proceedings of the IMA summer program, Minneapolis, MN, USA, July 17–August 4, 2006. New York, NY: Springer (ISBN 978-0-387-73830-7/hbk). The IMA Volumes in Mathematics and its Applications 144, 127-149 (2008). Reviewer: Hirokazu Nishimura (Tsukuba) MSC: 58H05 53A55 × Cite Format Result Cite Review PDF
Sardanashvily, G. Graded infinite order jet manifolds. (English) Zbl 1142.58005 Int. J. Geom. Methods Mod. Phys. 4, No. 8, 1335-1362 (2007). Reviewer: Miroslav Doupovec (Brno) MSC: 58A20 58E30 58J10 55N30 70S05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nong Quoc Chinh A presentation of the elements of the quotient sheaves \(\Omega_r^k/\Theta_r^k\) in variational sequences. (English) Zbl 1128.58011 Vietnam J. Math. 33, No. 3, 271-281 (2005). Reviewer: Miroslav Doupovec (Brno) MSC: 58E30 58J10 58A99 × Cite Format Result Cite Review PDF
Bashkirov, D.; Giachetta, G.; Mangiarotti, L.; Sardanashvily, G. The antifield Koszul-Tate complex of reducible Noether identities. (English) Zbl 1111.70026 J. Math. Phys. 46, No. 10, 103513, 19 p. (2005). MSC: 70S10 70S05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Krbek, Michael; Musilová, Jana Representation of the variational sequence by differential forms. (English) Zbl 1085.58014 Acta Appl. Math. 88, No. 2, 177-199 (2005). Reviewer: Boris S. Kruglikov (Tromsø) MSC: 58E30 58A20 53C65 58A10 × Cite Format Result Cite Review PDF Full Text: DOI
Reyes, Enrique G. On covariant phase space and the variational bicomplex. (English) Zbl 1061.37035 Int. J. Theor. Phys. 43, No. 5, 1267-1286 (2004). MSC: 37J05 70S05 81S10 × Cite Format Result Cite Review PDF Full Text: DOI
Reyes, Enrique G. On phase spaces and the variational bicomplex (after G. Zuckerman). (English) Zbl 1065.37046 Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 5th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 5–12, 2003. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-8-7/pbk). 189-202 (2004). Reviewer: Mircea Craioveanu (Timişoara) MSC: 37K05 70S05 53D05 37K10 × Cite Format Result Cite Review PDF Full Text: EMIS
Kogan, Irina A.; Olver, Peter J. Invariant Euler–Lagrange equations and the invariant variational bicomplex. (English) Zbl 1034.53015 Acta Appl. Math. 76, No. 2, 137-193 (2003). Reviewer: Josef Janyška (Brno) MSC: 53A55 58J70 58E40 35A30 49S05 58A20 × Cite Format Result Cite Review PDF Full Text: DOI
Aldrovandi, Ettore Homological algebra of multivalued action functionals. (English) Zbl 1022.58008 Lett. Math. Phys. 60, No. 1, 47-58 (2002). Reviewer: George F.Nassopoulos (Athens) MSC: 58E30 18G40 55N30 55U05 70S05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sardanashvily, Gennadi Cohomology of the variational complex in the class of exterior forms of finite jet order. (English) Zbl 1006.58013 Int. J. Math. Math. Sci. 30, No. 1, 39-47 (2002). Reviewer: Jan Chrastina (Brno) MSC: 58E30 58A20 55N30 × Cite Format Result Cite Review PDF Full Text: DOI EuDML Link
Manno, Gianni; Vitolo, Raffaele Variational sequences on finite order jets of submanifolds. (English) Zbl 1037.58002 Kowalski, Oldřich (ed.) et al., Differential geometry and its applications. Proceedings of the 8th international conference, Opava, Czech Republic, August 27–31, 2001. Opava: Silesian University at Opava (ISBN 80-7248-166-5/hbk). Math. Publ. (Opava) 3, 435-446 (2001). Reviewer: Vasile Oproiu (Iaşi) MSC: 58A20 58E99 58J10 × Cite Format Result Cite Review PDF Full Text: arXiv
Juráš, Martin Towards a solution of the inverse problem of the calculus of variations for scalar ordinary differential equations. (English) Zbl 1055.49023 Kowalski, Oldřich (ed.) et al., Differential geometry and its applications. Proceedings of the 8th international conference, Opava, Czech Republic, August 27–31, 2001. Opava: Silesian University at Opava (ISBN 80-7248-166-5/hbk). Math. Publ. (Opava) 3, 425-434 (2001). Reviewer: Mircea Crâşmăreanu (Iaşi) MSC: 49N45 34A26 34A55 58E30 × Cite Format Result Cite Review PDF
Kogan, Irina A.; Olver, Peter J. The invariant variational bicomplex. (English) Zbl 1004.58009 Leslie, Joshua A. (ed.) et al., The geometrical study of differential equations. NFS-CBMS conference, Washington, DC, USA, June 20-25, 2000. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 285, 131-144 (2001). Reviewer: Wiesław Olȩdzki (Białystok) MSC: 58E40 58A20 58J70 35A30 53A55 49S05 × Cite Format Result Cite Review PDF
Juráš, Martin The inverse problem of the calculus of variations for sixth- and eighth-order scalar ordinary differential equations. (English) Zbl 0991.49027 Acta Appl. Math. 66, No. 1, 25-39 (2001). Reviewer: Ion Mihai (Bucureşti) MSC: 49N45 34A55 53B50 × Cite Format Result Cite Review PDF Full Text: DOI
Fatibene, L.; Francaviglia, M.; Palese, M. Conservation laws and variational sequences in gauge-natural theories. (English) Zbl 0988.58006 Math. Proc. Camb. Philos. Soc. 130, No. 3, 555-569 (2001). Reviewer: I.Kolář (Brno) MSC: 58E30 58A32 70S15 70S10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mangiarotti, L.; Sardanashvily, G. Connections in classical and quantum field theory. (English) Zbl 1053.53022 Singapore: World Scientific (ISBN 981-02-2013-8/hbk). x, 504 p. (2000). Reviewer: Hirokazu Nishimura (Tsukuba) MSC: 53-02 53C05 53D50 53D55 58-02 70Sxx 81T70 81T75 × Cite Format Result Cite Review PDF
Marvan, Michal Geometric aspects of S-integrability. (English) Zbl 1020.58025 Krupka, D. (ed.), Proceedings of the seminar on differential geometry, Opava, Czech Republic, 2000. Opava: Silesian University at Opava. Math. Publ. (Opava). 2, 131-144 (2000). MSC: 58J72 58J99 58J10 × Cite Format Result Cite Review PDF
Alonso Blanco, Ricardo J. \(\mathcal D\)-modules, contact valued calculus and Poincare-Cartan form. (English) Zbl 1011.58011 Czech. Math. J. 49, No. 3, 585-606 (1999). Reviewer: Ivan Kolář (Brno) MSC: 58E30 58A20 58J10 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Krupka, Demeter Variational sequences and variational bicomplexes. (English) Zbl 0942.58028 Kolář, Ivan (ed.) et al., Differential geometry and applications. Proceedings of the 7th international conference, DGA 98, and satellite conference of ICM in Berlin, Brno, Czech Republic, August 10-14, 1998. Brno: Masaryk University. 525-531 (1999). MSC: 58E99 58A15 × Cite Format Result Cite Review PDF Full Text: EMIS
Vitolo, Raffaele On different geometric formulations of Lagrangian formalism. (English) Zbl 0930.58001 Differ. Geom. Appl. 10, No. 3, 225-255 (1999). Reviewer: R.Vitolo (Lecce) MSC: 58A12 58A20 58E30 58J10 × Cite Format Result Cite Review PDF Full Text: DOI
Vitolo, Raffaele A new infinite order formulation of variational sequences. (English) Zbl 0970.58002 Arch. Math., Brno 34, No. 4, 483-504 (1998). Reviewer: Ivan Kolář (Brno) MSC: 58A12 58A20 58E30 58J10 × Cite Format Result Cite Review PDF Full Text: EuDML
Stasheff, Jim The (secret?) homological algebra of the Batalin-Vilkovisky approach. (English) Zbl 0969.17012 Henneaux, Marc (ed.) et al., Secondary calculus and cohomological physics. Proceedings of a conference, Moscow, Russia, August 24-31, 1997. Providence, RI: AMS, American Mathematical Society. Contemp. Math. 219, 195-210 (1998). Reviewer: Johannes Huebschmann (Villeneuve d’Ascq) MSC: 17B55 16E45 81T70 37K25 18G55 70H03 70H33 70H45 70H50 × Cite Format Result Cite Review PDF Full Text: arXiv
Chrastina, Jan The formal theory of differential equations. (English) Zbl 0906.35002 Folia Facultatis Scientiarum Naturalium Universitatis Masarykianae Brunensis. Mathematica. 6. Brno: Masaryk University. x, 296 p. (1998). Reviewer: Werner M.Seiler (Mannheim) MSC: 35-02 35A30 35G20 49N45 58J70 58H05 × Cite Format Result Cite Review PDF
Torre, Charles G. Spinors, jets, and the Einstein equations. (English) Zbl 0912.53062 Braham, Stephen P. (ed.) et al., The 6th Canadian conference on General relativity and relativistic astrophysics. 6th CCRRA, University of New Brunswick, Fredericton, NJ, USA, May 25–27, 1995. Providence, RI: AMS, American Mathematical Society. Fields Inst. Commun. 15, 125-136 (1997). Reviewer: G.Pripoae (Bucureşti) MSC: 53Z05 83C05 83C60 58A20 × Cite Format Result Cite Review PDF Full Text: arXiv
Fels, M. E. The inverse problem of the calculus of variations for scalar fourth-order ordinary differential equations. (English) Zbl 0879.34016 Trans. Am. Math. Soc. 348, No. 12, 5007-5029 (1996). MSC: 34A55 49N45 53B50 × Cite Format Result Cite Review PDF Full Text: DOI
Anderson, Ian M.; Kamran, Niky Conservation laws and the variational bicomplex for second-order scalar hyperbolic equations in the plane. (English) Zbl 0848.58043 Acta Appl. Math. 41, No. 1-3, 135-144 (1995). Reviewer: M.Biroli (Monza) MSC: 58J45 35A30 35L65 × Cite Format Result Cite Review PDF Full Text: DOI
Dickey, L. A. On exactness of the variational bicomplex. (English) Zbl 0771.58043 Mathematical aspects of classical field theory, Proc. AMS-IMS-SIAM Jt. Summer Res. Conf., Seattle/WA (USA) 1991, Contemp. Math 132, 307-315 (1992). Reviewer: H.Schröder (Dortmund) MSC: 58J10 57R20 × Cite Format Result Cite Review PDF
Saunders, D. J. The geometry of jet bundles. (English) Zbl 0665.58002 London Mathematical Society Lecture Note Series, 142. Cambridge etc.: Cambridge University Press. 293 p. £20.00; $ 29.95 (1989). Reviewer: I.Kolář MSC: 58A20 58-02 49Q99 58A15 49S05 × Cite Format Result Cite Review PDF
Anderson, Ian M. Aspects of the inverse problem to the calculus of variations. (English) Zbl 0674.58017 Arch. Math., Brno 24, No. 4, 181-202 (1988). Reviewer: G.Toth MSC: 58E30 × Cite Format Result Cite Review PDF Full Text: EuDML