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On mKdV equations related to the affine Kac-Moody algebra \(A_5^{(2)}\). (English) Zbl 1343.35208

Summary: We have derived a new system of modified Korteweg-de Vries (mKdV)-type equations which can be related to the affine Lie algebra \(A^{(2)}_5\). This system of partial differential equations is integrable via the inverse scattering method. It admits a Hamiltonian formulation and the corresponding Hamiltonian is also given. The Riemann-Hilbert problem for the Lax operator is formulated and its spectral properties are discussed.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
35Q15 Riemann-Hilbert problems in context of PDEs
22E46 Semisimple Lie groups and their representations
53C35 Differential geometry of symmetric spaces
57S20 Noncompact Lie groups of transformations
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