DOMAINES DE RECHERCHE
Physique mathématique et analyse des symétries des équations aux dérivées partielles
1. Analyse de groupe des équations aux dérivées partielles
2. Méthodes géométriques de résolution des EDPs
3. Surfaces plongées dans des algèbres de Lie et des espaces homogènes obtenus par les applications harmoniques
4. Systèmes intégrables et modèles supersymétriques
FIELD OF RESEARCH
Mathematical physics and symmetry analysis of partial differential equations
1. Group analysis of partial differential equations
2. Geometric methods for solving PDEs
3. Surfaces immersed in Lie algebras and homogeneous spaces obtained via harmonic maps
4. Integrable systems and supersymmetric models
Quelques publications récentes
Some recent publications
- S. Bertrand, A.M. Grundland (2016) Supersymmetric versions of the Fokas-Gel'fand formula for immersion, J. Phys. A: Math. Theor. 49, 305201
- A.M. Grundland, D. Levi, L. Martina (2016), On immersion formulas for soliton surfaces, Acta. Polytechnica (Czech Technical University), 56, 3, ISSN 1210-2709, 180-192.
- R. Conte, A.M. Grundland (2016) Reductions of Gauss-Codazzi equations, Studies in Appl. Math. (22pp), DOI: 10.1111/sapm.12121
- S. Bertrand, A.M. Grundland, A. J. Hariton (2015), On the integrability of supersymmetric versions of the structural equations for conformally parametrized surfaces, in Symmetry, Integrability and Geometry. Methods and Applications, SIGMA 11, 046 (16pp) [arXiv:1502.02948v3]
- A.M. Grundland, D. Riglioni (2015), Classical-quantum correspondence for shape-invariant systems, J. Phys. A: Math. Theor. 48, 245201 (15pp) doi:10.1088/1751-8113/48/24/245201
- S. Bertrand, A.M. Grundland, A. J. Hariton (2015), Supersymmetric versions of the equations of conformally parametrized surfaces, J. Phys. A: Math. Theor. 48, 175208 (37pp) doi:10.1088/1751-8113/48/17/175208
- A.M. Grundland, V. Lamothe (2014), Solutions of first-order quasilinear systems expressed in Riemann invariants, Acta Appl. Math., Springer Sc. doi:10.1007/s10440-014-9999-4 pp 1-29
- A.M. Grundland, V. Lamothe (2014), Multimode solutions of first-order quasilinear systems obtained from Riemann invariants, Acta Appl. Math., Springer Sc. doi:10.1007/s10440-014-9958-0 pp 1-32
- A.M. Grundland, S. Post, D. Riglioni (2014), Soliton surfaces and generalized symmetries of integrable systems, J. Phys. A: Math. Theor. 47, 015201 (14pp) doi:10.1088/1751-8113/47/1/015201
- A.M. Grundland, A. J. Hariton (2013), Supersymmetric version of the Euler system and its invariant solutions, Symmetry 5, 253-270 doi 10.3390/sym5030253
- P. P. Goldstein, A.M. Grundland, S. Post (2012), Soliton surfaces associated with sigma models; differential and algebraic aspects, J. Phys. A: Math. Theor. 45, 395208 (19pp) doi:10.1088/1751-8113/45/39/395208
- A.M. Grundland, S. Post (2012), Soliton surfaces via a zero-curvature representation of differential equations, J. Phys. A: Math. Theor. 45, 115204 (24pp); Corrigendum (2012), J. Phys. A: Math. Theor. 45, 419501 (1pp) doi:10.1088/1751-8113/45/11/115204
- S. Post, A.M. Grundland (2012), Analysis of $\mathbb{C}P^{N-1}$ sigma models via projective structure, Nonlinearity 25, 1-36 doi:10.1088/0951-7715/25/1/1
- A.M. Grundland, S. Post (2012), Surfaces immersed in Lie algebras associated with elliptic integrals, J. Phys. A: Math. Theor. 45, 015204 (20pp) doi:10.1088/1751-8113/45/1/015204
- A.M. Grundland, A.J. Hariton (2011), Supersymmetric formulation of polytropic gas dynamics and its invariant solutions, J. Math. Phys. 52, 4, 043501 (21pp).
- A.M. Grundland, S. Post (2011), Soliton surfaces associated with generalized symmetries of integrable equations, J. Phys. A: Math. Theor. 44, 165203 (31pp), selected for inclusion in {\bf IOP Select} doi:10.1088/1751-8113/44/16/165203
- A.M. Grundland, A.J. Hariton, L. Snobl (2011), Invariant solutions of supersymmetric nonlinear wave equations, J. Phys. A: Math. Theor. 44, 085204 (22pp), selected for inclusion in {\bf IOP Select} doi:10.1088/1751-8113/44/8/085204
- P.P. Goldstein, A.M. Grundland (2010), Invariant recurrence relations for $\mathbb{C}P^{N-1}$ models, J. Phys. A: Math. Theor. 43, 265206 (18pp) doi:10.1088/1751-8113/43/26/265206
- A. M. Grundland, B. Huard (2010), Conditional symmetries and Riemann invariants for inhomogeneous hydrodynamic-type systems, J. Phys. A : Math. Theor. 43, 455217 (16pp) doi:10.1088/1751-8113/43/45/455217
Liste complète des publications Full Listing of Publications
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