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Complete integrability of the coupled KdV-mKdV system. (English) Zbl 1184.37054
Morimoto, Tohru (ed.) et al., Lie groups, geometric structures and differential equations—one hundred years after Sophus Lie. Based on the international conference on the occasion of the centennial after the death of Sophus Lie (1842–1899), Kyoto and Nara, Japan, December 1999. Tokyo: Mathematical Society of Japan (ISBN 4-931469-21-3/hbk). Adv. Stud. Pure Math. 37, 151-171 (2002).
Summary: The coupled KdV-mKdV system arises as the classical part of one of superextensions of the KdV equation. For this system, we prove its complete integrability, i.e., existence of a recursion operator and of infinite series of symmetries.
For the entire collection see [Zbl 1011.00031].

MSC:
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35A30 Geometric theory, characteristics, transformations in context of PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
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