Integrable Hamiltonian Hierarchies: Spectral and Geometric Methods

By V. Gerdjikov, G. Vilasi, A. Yanovski. 2008

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Application of the Riemann–Hilbert approach to the multicomponent AKNS integrable hierarchies (2019, methodology): “We point out that when the underlying matrix loop algebra in the zero curvature formulation is simple, the associated zero curvature equations engender typical integrable hierarchies [28,10]; when semisimple, the associated zero curvature equations generate a collection of different integrable hiera”
The inverse scattering transform and soliton solutions of a combined modified Korteweg–de Vries equation (2019, background): “When the underlying matrix loop algebra in the zero curvature formulation is simple, the associated zero curvature equations engender classical integrable hierarchies [7,13]; when semisimple, the associated zero curvature equations generate a collection of different integrable hierarchies; and when ”