Аннотация:
Для произвольного NN построена 2N2N-компонентная интегрируемая система второго порядка со спектральным параметром, лежащим на кривой рода g=1+(N−3)2N−2g=1+(N−3)2N−2. Потоки нечетного порядка допускают NN-компонентные редукции, которые при N=3N=3 совпадают с потоками нечетного порядка из иерархии уравнения Ландау–Лифшица.
Образец цитирования:
И. З. Голубчик, В. В. Соколов, “Многокомпонентное обобщение иерархии уравнения Ландау–Лифшица”, ТМФ, 124:1 (2000), 62–71; Theoret. and Math. Phys., 124:1 (2000), 909–917
К. Р. Аталиков, А. В. Зотов, “Калибровочная эквивалентность между (1+1)(1+1)-мерными теориями поля Калоджеро–Мозера–Сазерленда и тригонометрическим уравнением Ландау–Лифшица старшего ранга”, ТМФ, 219:3 (2024), 545–561; K. R. Atalikov, A. V. Zotov, “Gauge equivalence of 1+11+1 Calogero–Moser–Sutherland field
theory and a higher-rank trigonometric Landau–Lifshitz model”, Theoret. and Math. Phys., 219:3 (2024), 1004–1017
Tihomir I. Valchev, Studies in Computational Intelligence, 1076, Advanced Computing in Industrial Mathematics, 2023, 166
K. Atalikov, A. Zotov, “Higher rank 1+11+1 integrable Landau–Lifshitz field theories from associative Yang–Baxter equation”, Письма в ЖЭТФ, 115:12 (2022), 809–810; K. Atalikov, A. Zotov, “Higher rank 1 + 1 integrable landauвђ“lifshitz field theories from the associative yangвђ“baxter equation”, JETP Letters, 115:12 (2022), 757–762
Valchev T., “Multicomponent Nonlinear Evolution Equations of the Heisenberg Ferromagnet Type: Local Versus Nonlocal Reductions”, Proceedings of the Twenty-Second International Conference on Geometry, Integrability and Quantization, Proceedings of the International Conference on Geometry Integrability and Quantization, 22, ed. Mladenov I. Pulov V. Yoshioka A., Inst Biophysics & Biomedical Engineering Bulgarian Acad Sciences, 2021, 274–285
Yanovski A.B., Valchev T.I., “Hermitian and Pseudo-Hermitian Reduction of the Gmv Auxiliary System. Spectral Properties of the Recursion Operators”, Advanced Computing in Industrial Mathematics (Bgsiam 2017), Studies in Computational Intelligence, 793, eds. Georgiev K., Todorov M., Georgiev I., Springer International Publishing Ag, 2019, 433–446
Valchev T., Yanovski A., “Solutions to a Vector Heisenberg Ferromagnet Equation Related to Symmetric Spaces”, Proceedings of the Twentieth International Conference on Geometry, Integrability and Quantization, eds. Mladenov I., Pulov V., Yoshioka A., Inst Biophysics & Biomedical Engineering Bulgarian Acad Sciences, 2019, 285–296
Skrypnyk T., “Reduction in Soliton Hierarchies and Special Points of Classical R-Matrices”, J. Geom. Phys., 130 (2018), 260–287
Valchev I T. Yanovski A.B., “Pseudo-Hermitian Reduction of a Generalized Heisenberg Ferromagnet Equation. II. Special Solutions”, J. Nonlinear Math. Phys., 25:3 (2018), 442–461
Sun XiaoWei, Wang YouDe, “New Geometric Flows on Riemannian Manifolds and Applications To Schrodinger-Airy Flows”, Sci. China-Math., 57:11 (2014), 2247–2272
Meshkov A. Sokolov V., “Vector Hyperbolic Equations on the Sphere Possessing Integrable Third-Order Symmetries”, Lett. Math. Phys., 104:3 (2014), 341–360
Song Chong, Yu Jie, “The Cauchy Problem of Generalized Landau-Lifshitz Equation Into S (N)”, Sci. China-Math., 56:2 (2013), 283–300
Igonin S., van de Leur J., Manno G., Trushkov V., “Infinite-Dimensional Prolongation Lie Algebras and Multicomponent Landau-Lifshitz Systems Associated with Higher Genus Curves”, J. Geom. Phys., 68 (2013), 1–26
М. Ю. Балахнев, “Дифференциальные подстановки первого порядка для уравнений интегрируемых в Sn”, Матем. заметки, 89:2 (2011), 178–189; M. Yu. Balakhnev, “First-Order Differential Substitutions for Equations Integrable on Sn”, Math. Notes, 89:2 (2011), 184–193
В. С. Герджиков, Г. Г. Граховски, А. В. Михайлов, Т. И. Валчев, “Рациональные пучки и рекурсионные операторы для интегрируемых уравнений на
симметричных пространствах типа A.III”, ТМФ, 167:3 (2011), 394–406; V. S. Gerdjikov, G. G. Grahovski, A. V. Mikhailov, T. I. Valchev, “Rational bundles and recursion operators for integrable equations on A.III-type symmetric spaces”, Theoret. and Math. Phys., 167:3 (2011), 740–750
Andrei V. Zotov, “1+1 Gaudin Model”, SIGMA, 7 (2011), 067, 26 pp.
Vladimir S. Gerdjikov, Georgi G. Grahovski, Alexander V. Mikhailov, Tihomir I. Valchev, “Polynomial Bundles and Generalised Fourier Transforms for Integrable Equations on A.III-type Symmetric Spaces”, SIGMA, 7 (2011), 096, 48 pp.
Valchev T.I., “On Certain Reductions of Integrable Equations on Symmetric Spaces”, International Workshop on Complex Structures, Integrability and Vector Fields, AIP Conference Proceedings, 1340, 2011, 154–164
Gerdjikov V.S., Mikhailov A.V., Valchev T.I., “Reductions of integrable equations on A.III-type symmetric spaces”, J. Phys. A: Math. Theor., 43:43 (2010), 434015