Аннотация:
A list of forty third-order exactly integrable two-field evolutionary systems is presented. Differential substitutions connecting various systems from the list are found. It is proved that all the systems can be obtained from only two of them. Examples of zero curvature representations with 4×44×4 matrices are presented.
Образец цитирования:
Anatoly G.G. Meshkov, Maxim Ju. Balakhnev, “Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions”, SIGMA, 4 (2008), 018, 29 pp.
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Эта публикация цитируется в следующих 10 статьяx:
М. Ю. Балахнев, “Результаты симметрийной классификации 2-полевых эволюционных систем 3-го порядка с постоянной сепарантой”, Ж. вычисл. матем. и матем. физ., 63:4 (2023), 596–613; M. Yu. Balakhnev, “Results of symmetry classification of 2-field third-order evolutionary systems with a constant separant”, Comput. Math. Math. Phys., 63:4 (2023), 564–581
Lou S.Y., “Alice-Bob Systems, (P)Over-Cap-(T)Over-Cap-(C)Over-Cap Symmetry Invariant and Symmetry Breaking Soliton Solutions”, J. Math. Phys., 59:8 (2018), 083507
Wang D.-Sh., Wei X., “Integrability and Exact Solutions of a Two-Component Korteweg-de Vries System”, Appl. Math. Lett., 51 (2016), 60–67
Wang D.-Sh., Liu J., Zhang Zh., “Integrability and equivalence relationships of six integrable coupled Korteweg-de Vries equations”, Math. Meth. Appl. Sci., 39:12 (2016), 3516–3530
Berkeley G., Igonin S., “Miura-type transformations for lattice equations and Lie group actions associated with Darboux?Lax representations”, J. Phys. A-Math. Theor., 49:27 (2016), 275201
М. Ю. Балахнев, “О дифференциальных подстановках для векторных обобщений мКдФ”, Матем. заметки, 98:2 (2015), 173–179; M. Yu. Balakhnev, “Differential Substitutions for Vectorial Generalizations of the mKdV Equation”, Math. Notes, 98:2 (2015), 204–209
А. Г. Мешков, В. В. Соколов, “Интегрируемые эволюционные уравнения с постоянной сепарантой”, Уфимск. матем. журн., 4:3 (2012), 104–154
Balakhnev M.Yu., Demskoi D.K., “Auto-Backlund Transformations and Superposition Formulas for Solutions of Drinfeld-Sokolov Systems”, Appl. Math. Comput., 219:8 (2012), 3625–3637
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
Mikhailov A. V., Sokolov V. V., “Symmetries of differential equations and the problem of integrability”, Lecture Notes in Physics, 767, 2009, 19–88
Цитирование в формате AMSBIB
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