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Multi-component generalizations of mKdV equation and nonassociative algebraic structures. (English) Zbl 1468.17040

Summary: Relations between triple Jordan systems and integrable multi-component models of the modified Korteveg-de Vries type are established. The most general model is related to a pair consisting of a triple Jordan system and a skew-symmetric bilinear operation. If this operation is a Lie bracket, then we arrive at the Lie-Jordan algebras [Speciality of Lie-Jordan algebras, J. Algebra 237, 621–636 (2001; Zbl 0988.17026)].

MSC:

17B80 Applications of Lie algebras and superalgebras to integrable systems
17C50 Jordan structures associated with other structures
35Q53 KdV equations (Korteweg-de Vries equations)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)

Citations:

Zbl 0988.17026
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References:

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