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Dirac constraints in field theory and exterior differential systems
1. | Instituto Balseiro and Centro Atómico Bariloche, Avda. E. Bustillo km. 9,5, S. C. de Bariloche, Argentina |
[1] |
Eduardo Martínez. Classical field theory on Lie algebroids: Multisymplectic formalism. Journal of Geometric Mechanics, 2018, 10 (1) : 93-138. doi: 10.3934/jgm.2018004 |
[2] |
Hernán Cendra, María Etchechoury, Sebastián J. Ferraro. An extension of the Dirac and Gotay-Nester theories of constraints for Dirac dynamical systems. Journal of Geometric Mechanics, 2014, 6 (2) : 167-236. doi: 10.3934/jgm.2014.6.167 |
[3] |
Ünver Çiftçi. Leibniz-Dirac structures and nonconservative systems with constraints. Journal of Geometric Mechanics, 2013, 5 (2) : 167-183. doi: 10.3934/jgm.2013.5.167 |
[4] |
Paul Bracken. Exterior differential systems and prolongations for three important nonlinear partial differential equations. Communications on Pure and Applied Analysis, 2011, 10 (5) : 1345-1360. doi: 10.3934/cpaa.2011.10.1345 |
[5] |
Marco Castrillón López, Mark J. Gotay. Covariantizing classical field theories. Journal of Geometric Mechanics, 2011, 3 (4) : 487-506. doi: 10.3934/jgm.2011.3.487 |
[6] |
Angelo B. Mingarelli. Nonlinear functionals in oscillation theory of matrix differential systems. Communications on Pure and Applied Analysis, 2004, 3 (1) : 75-84. doi: 10.3934/cpaa.2004.3.75 |
[7] |
Wenmin Gong, Guangcun Lu. On coupled Dirac systems. Discrete and Continuous Dynamical Systems, 2017, 37 (8) : 4329-4346. doi: 10.3934/dcds.2017185 |
[8] |
María Barbero Liñán, Hernán Cendra, Eduardo García Toraño, David Martín de Diego. Morse families and Dirac systems. Journal of Geometric Mechanics, 2019, 11 (4) : 487-510. doi: 10.3934/jgm.2019024 |
[9] |
Kai Du, Jianhui Huang, Zhen Wu. Linear quadratic mean-field-game of backward stochastic differential systems. Mathematical Control and Related Fields, 2018, 8 (3&4) : 653-678. doi: 10.3934/mcrf.2018028 |
[10] |
Jiakun Liu, Neil S. Trudinger. On the classical solvability of near field reflector problems. Discrete and Continuous Dynamical Systems, 2016, 36 (2) : 895-916. doi: 10.3934/dcds.2016.36.895 |
[11] |
Harald Markum, Rainer Pullirsch. Classical and quantum chaos in fundamental field theories. Conference Publications, 2003, 2003 (Special) : 596-603. doi: 10.3934/proc.2003.2003.596 |
[12] |
Melvin Leok, Diana Sosa. Dirac structures and Hamilton-Jacobi theory for Lagrangian mechanics on Lie algebroids. Journal of Geometric Mechanics, 2012, 4 (4) : 421-442. doi: 10.3934/jgm.2012.4.421 |
[13] |
Matthias Hieber. Remarks on the theory of Oldroyd-B fluids in exterior domains. Discrete and Continuous Dynamical Systems - S, 2013, 6 (5) : 1307-1313. doi: 10.3934/dcdss.2013.6.1307 |
[14] |
Ruikuan Liu, Tian Ma, Shouhong Wang, Jiayan Yang. Thermodynamical potentials of classical and quantum systems. Discrete and Continuous Dynamical Systems - B, 2019, 24 (4) : 1411-1448. doi: 10.3934/dcdsb.2018214 |
[15] |
Luca Consolini, Alessandro Costalunga, Manfredi Maggiore. A coordinate-free theory of virtual holonomic constraints. Journal of Geometric Mechanics, 2018, 10 (4) : 467-502. doi: 10.3934/jgm.2018018 |
[16] |
Claude Bardos, Nicolas Besse. The Cauchy problem for the Vlasov-Dirac-Benney equation and related issues in fluid mechanics and semi-classical limits. Kinetic and Related Models, 2013, 6 (4) : 893-917. doi: 10.3934/krm.2013.6.893 |
[17] |
Yanheng Ding, Xiaojing Dong, Qi Guo. On multiplicity of semi-classical solutions to nonlinear Dirac equations of space-dimension $ n $. Discrete and Continuous Dynamical Systems, 2021, 41 (9) : 4105-4123. doi: 10.3934/dcds.2021030 |
[18] |
Jun Moon. Linear-quadratic mean-field type stackelberg differential games for stochastic jump-diffusion systems. Mathematical Control and Related Fields, 2022, 12 (2) : 371-404. doi: 10.3934/mcrf.2021026 |
[19] |
Jaume Llibre, Clàudia Valls. Hopf bifurcation for some analytic differential systems in $\R^3$ via averaging theory. Discrete and Continuous Dynamical Systems, 2011, 30 (3) : 779-790. doi: 10.3934/dcds.2011.30.779 |
[20] |
Kyeong-Hun Kim, Kijung Lee. A weighted $L_p$-theory for second-order parabolic and elliptic partial differential systems on a half space. Communications on Pure and Applied Analysis, 2016, 15 (3) : 761-794. doi: 10.3934/cpaa.2016.15.761 |
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