Dr. G.F. (Gerard) Helminck
Faculteit der Natuurwetenschappen, Wiskunde en Informatica
Korteweg-de Vries Instituut
Bezoekadres
- Science Park 107
- Kamernummer: F3.15
Postadres
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Postbus 94248
1090 GE Amsterdam
Contactgegevens
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Publicaties
2025
- Helminck, A. G., & Helminck, G. F. (2025). A construction of solutions of an integrable deformation of a commutative Lie algebra of skew hermitian Z×Z-matrices. Indagationes Mathematicae, 36(1), Article 42-60. https://doi.org/10.1016/j.indag.2024.04.001 [details]
2024
- Helminck, G. F., Poberezhny, V. A., & Polenkova, S. V. (2024). Darboux transformations for the discrete versions of the KP and strict KP hierarchies. Theoretical and Mathematical Physics (Russian Federation), 221(3), 2031-2048. https://doi.org/10.1134/S0040577924120031 [details]
2023
Helminck, G. F. (2023). Cauchy problems related to integrable matrix hierarchies. Theoretical and Mathematical Physics, 216(2), 1124-1141. https://doi.org/10.1134/S0040577923080056 [details]- Helminck, G. F., & Weenink, J. A. (2023). Scaling Invariance of the k[S]-Hierarchy and Its Strict Version. Lobachevskii Journal of Mathematics, 44(9), 3927-3940. https://doi.org/10.1134/S199508022309010X [details]
2021
- Helminck, G. F., & Panasenko, E. A. (2021). Darboux transformations for the strict KP hierarchy. Theoretical and Mathematical Physics, 206, 296-314. https://doi.org/10.1134/S004057792103003X [details]
2020
- Helminck, G. F., & Panasenko, E. A. (2020). Properties of the algebra psd related to integrable hierarchies. Russian Universities Reports. Mathematics, 25(130), 183-195. https://doi.org/10.20310/2686-9667-2020-25-130-183-195 [details]
- Helminck, G. F., & Panasenko, E. A. (2020). Reductions of the strict KP hierarchy. Theoretical and Mathematical Physics(Russian Federation), 205(2), 1411-1425. https://doi.org/10.1134/S0040577920110021 [details]
- Helminck, G. F., & Panasenko, E. A. (2020). Scaling invariance of the strict KP hierarchy. Russian Universities Reports. Mathematics, 25(131), 331-340. https://doi.org/10.20310/2686-9667-2020-25-131-331-340 [details]
- Helminck, G. F., & Weenink, J. A. (2020). Integrable hierarchies in the N×N-matrices related to powers of the shift operator. Journal of Geometry and Physics, 148, Article 103560. https://doi.org/10.1016/j.geomphys.2019.103560 [details]
- Helminck, G. F., Poberezhny, V. A., & Polenkova, S. V. (2020). Extensions of the discrete KP hierarchy and its strict version. Theoretical and Mathematical Physics(Russian Federation), 204(3), 1140-1153. https://doi.org/10.1134/S0040577920090044 [details]
2019
- Helminck, G. F. (2019). A Geometric Construction of Solutions of the Strict h-Hierarchy. Theoretical and Mathematical Physics(Russian Federation), 200(1), 985-1005. https://doi.org/10.1134/S0040577919070043 [details]
- Helminck, G. F., & Panasenko, E. A. (2019). Expressions in Fredholm Determinants for Solutions of the Strict KP Hierarchy. Theoretical and Mathematical Physics(Russian Federation), 199(2), 637-651. https://doi.org/10.1134/S0040577919050027 [details]
- Helminck, G. F., & Panasenko, E. A. (2019). Geometric Solutions of the Strict KP Hierarchy. Theoretical and Mathematical Physics(Russian Federation), 198(1), 48-68. https://doi.org/10.1134/S0040577919010045 [details]
- Helminck, G. F., & Twilt, F. (2019). Newton flows for elliptic functions III & IV: Pseudo Newton graphs: bifurcation and creation of flows. European Journal of Mathematics, 5(4), 1364-1395. https://doi.org/10.1007/s40879-018-0289-y [details]
- Helminck, G. F., Poberezhny, V. A., & Polenkova, S. V. (2019). Strict Versions of Integrable Hierarchies in Pseudodifference Operators and the Related Cauchy Problems. Theoretical and Mathematical Physics(Russian Federation), 198(2), 197-214. https://doi.org/10.1134/S004057791902003X [details]
2018
- Helminck, G. F., & Twilt, F. (2018). Newton flows for elliptic functions I Structural stability: characterization & genericity. Complex Variables and Elliptic Equations, 63(6), 815-835. https://doi.org/10.1080/17476933.2017.1350853 [details]
- Helminck, G. F., Poberezhny, V. A., & Polenkova, S. V. (2018). A geometric construction of solutions of the strict dKP(Λ0) hierarchy. Journal of Geometry and Physics, 131, 189-203. https://doi.org/10.1016/j.geomphys.2018.05.015 [details]
2017
- Helminck, G. F. (2017). An integrable hierarchy including the AKNS hierarchy and its strict version. Theoretical and Mathematical Physics(Russian Federation), 192(3), 1324-1336. https://doi.org/10.1134/S0040577917090045 [details]
- Helminck, G. F. (2017). Integrable deformations in the matrix pseudo differential operators. Journal of Geometry and Physics, 113, 104-116. https://doi.org/10.1016/j.geomphys.2016.04.024 [details]
- Helminck, G. F. (2017). Strict versions of various matrix hierarchies related to sln-loops and their combinations. Quarterly Physics Review, 3(2), Article 1408. http://journals.ke-i.org/index.php/qpr/article/view/1408 [details]
- Helminck, G. F., & Twilt, F. (2017). Newton flows for elliptic functions II: Structural stability: classification and representation. European Journal of Mathematics, 3(3), 691-727. https://doi.org/10.1007/s40879-017-0146-4 [details]
2016
- Helminck, G. F. (2016). The Strict AKNS Hierarchy: Its Structure and Solutions. Advances in Mathematical Physics, 2016, Article 3649205. https://doi.org/10.1155/2016/3649205 [details]
2015
- Helminck, G. F., Panasenko, E. A., & Polenkova, S. V. (2015). Bilinear equations for the strict KP hierarchy. Theoretical and Mathematical Physics, 185(3), 1803-1815. https://doi.org/10.1007/s11232-015-0380-1 [details]
2014
- Helminck, G. F., & Helminck, A. G. (2014). Infinite dimensional symmetric spaces and Lax equations compatible with the infinite Toda chain. Journal of Geometry and Physics, 85, 60-74. https://doi.org/10.1016/j.geomphys.2014.05.023 [details]
- Helminck, G. F., Helminck, A. G., & Panasenko, E. A. (2014). Cauchy problems related to integrable deformations of pseudo differential operators. Journal of Geometry and Physics, 85, 196-205. https://doi.org/10.1016/j.geomphys.2014.05.004 [details]
2013
- Helminck, G. F., Helminck, A. G., & Panasenko, E. A. (2013). Integrable deformations in the algebra of pseudodifferential operators from a Lie algebraic perspective. Theoretical and Mathematical Physics, 174(1), 134-153. https://doi.org/10.1007/s11232-013-0011-7 [details]
2012
- Helminck, G. F., & Opimakh, A. V. (2012). The zero curvature form of integrable hierarchies in the Z x Z-matrices. Algebra Colloquium, 19(2), 237-262. https://doi.org/10.1142/S1005386712000168 [details]
- Helminck, G. F., Panasenko, E. A., & Sergeeva, A. O. (2012). A formal infinite dimensional Cauchy problem and its relation to integrable hierarchies. In M. L. Ge, C. Bai, & N. Jing (Eds.), Quantized Algebra and Physics: Proceedings of the International Workshop on Quantizided Algebra and Physics, Tianjin, China, 23 - 26 July 2009 (pp. 89-108). World Scientific. https://doi.org/10.1142/9789814340458_0005 [details]
2011
- Gontsov, R. R., Poberezhnyi, V. A., & Helminck, G. F. (2011). On deformations of linear differential systems. Russian Mathematical Surveys, 66(1), 63-105. https://doi.org/10.1070/RM2011v066n01ABEH004728 [details]
- Helminck, G. F., Helminck, A. G., & Opimakh, A. V. (2011). Equivalent forms of multi component Toda hierarchies. Journal of Geometry and Physics, 61(4), 847-873. https://doi.org/10.1016/j.geomphys.2010.11.013 [details]
- Helminck, G. F., Helminck, A. G., & Opimakh, A. V. (2011). Reprint of: equivalent forms of multi component Toda hierarchies. Journal of Geometry and Physics, 61(9), 1755-1781. https://doi.org/10.1016/j.geomphys.2011.06.012 [details]
2010
- Helminck, G. F., & Panasenko, E. A. (2010). An algebraic characterization of the bilinear relations of the matrix hierarchy associated with a commutative algebra of k×k-matrices. Acta Applicandae Mathematicae, 109(1), 45-59. https://doi.org/10.1007/s10440-009-9440-6 [details]
- Helminck, G. F., & Poberezhny, V. A. (2010). Moving poles of meromorphic linear systems on ℙ1(ℂ) in the complex plane. Theoretical and Mathematical Physics, 165(3), 1637-1649. https://doi.org/10.1007/s11232-010-0134-z [details]
- Helminck, G. F., & Poberezhny, V. A. (2010). Подвижные полюсы мероморфных линейных систем на P1(C) в комплексной плоскости. Теоретическая и математическая физика, 165(3), 472-487. https://doi.org/10.4213/tmf6588 [details]
- Helminck, G. F., Helminck, A. G., & Opimakh, A. V. (2010). The relative frame bundle of an infinite-dimensional flag variety and solutions of integrable hierarchies. Theoretical and Mathematical Physics, 165(3), 1610-1636. https://doi.org/10.1007/s11232-010-0133-0 [details]
- Helminck, G. F., Helminck, A. G., & Opimakh, A. V. (2010). Относительное расслоение реперов бесконечномерного многообразия флагов и решения интегрируемых иерархий. Теоретическая и математическая физика, 165(3), 440-471. http://mi.mathnet.ru/tmf6587 [details]
2008
- Helminck, G. F., & Opimakh, A. V. (2008). Composition series for representations of the generalized Lorentz group associated with a cone. Bulgarian Journal of Physics, 35, 335-351. [details]
- Helminck, G. F., & Polenkova, S. V. (2008). An analytic framework for the two-dimensional infinite Toda hierarchy associated with a commutative algebra. Theoretical and Mathematical Physics, 155(1), 659-672. https://doi.org/10.1007/s11232-008-0055-2 [details]
- Twilt, F., Helminck, G. F., Snuverink, M., & van den Brug, L. (2008). Newton flows for elliptic functions: A pilot study. Optimization, 57(1), 113-134. https://doi.org/10.1080/02331930701778965 [details]
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Helminck, G. F. (2023). Cauchy problems related to integrable matrix hierarchies. Theoretical and Mathematical Physics, 216(2), 1124-1141.