Gerdjikov, Vladimir S.; Mladenov, Dimitar M.; Stefanov, Aleksander A.; Varbev, Stanislav K. On mKdV equations related to the affine Kac-Moody algebra \(A_5^{(2)}\). (English) Zbl 1343.35208 J. Geom. Symmetry Phys. 39, 17-31 (2015). 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. Cited in 5 Documents 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 Keywords:affine Kac-Moody algebras; modified KdV equations; Riemann-Hilbert problems PDFBibTeX XMLCite \textit{V. S. Gerdjikov} et al., J. Geom. Symmetry Phys. 39, 17--31 (2015; Zbl 1343.35208) Full Text: DOI arXiv