Publication:
Recursion operators and hierarchies of mKdV equations related to the Kac–Moody algebras D(1)4, D4(2), and D4(3)

Дата
2020
Авторы
Stefanov, A. A.
Iliev, I. D.
Boyadjiev, G. P.
Smirnov, A. O.
Gerdjikov, V. S.
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Научные группы
Организационные подразделения
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Институт лазерных и плазменных технологий
Стратегическая цель Института ЛаПлаз – стать ведущей научной школой и ядром развития инноваций по лазерным, плазменным, радиационным и ускорительным технологиям, с уникальными образовательными программами, востребованными на российском и мировом рынке образовательных услуг.
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Аннотация
© 2020, Pleiades Publishing, Ltd.Abstract: We construct three nonequivalent gradings in the algebra D4 (Formula presented.). so(8). The first is the standard grading obtained with the Coxeter automorphism C1 = Sα2Sα1Sα3Sα4 using its dihedral realization. In the second, we use C2 = C1R, where R is the mirror automorphism. The third is C3 = Sα2Sα1T, where T is the external automorphism of order 3. For each of these gradings, we construct a basis in the corresponding linear subspaces g(k), the orbits of the Coxeter automorphisms, and the related Lax pairs generating the corresponding modified Korteweg–de Vries (mKdV) hierarchies. We find compact expressions for each of the hierarchies in terms of recursion operators. Finally, we write the first nontrivial mKdV equations and their Hamiltonians in explicit form. For D4(1), these are in fact two mKdV systems because the exponent 3 has the multiplicity two in this case. Each of these mKdV systems consists of four equations of third order in ∂x. For D4(2), we have a system of three equations of third order in ∂x. For D4(3), we have a system of two equations of fifth order in ∂x.
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Recursion operators and hierarchies of mKdV equations related to the Kac–Moody algebras D(1)4, D4(2), and D4(3) / Stefanov, A.A. [et al.] // Theoretical and Mathematical Physics(Russian Federation). - 2020. - 204. - № 3. - P. 1110-1129. - 10.1134/S0040577920090020
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https://www.doi.org/10.1134/S0040577920090020
 https://www.scopus.com/record/display.uri?eid=2-s2.0-85091484570&origin=resultslist
 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=Alerting&SrcApp=Alerting&DestApp=WOS_CPL&DestLinkType=FullRecord&UT=WOS:000572663400002
 https://openrepository.mephi.ru/handle/123456789/22372
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