Darboux Transformations for the KP Hierarchy in the Segal-Wilson Setting

DOI10.4153/CJM-2001-012-4zbMath0970.22017OpenAlexW3021592144MaRDI QIDQ2715671

Gerardus F. Helminck, Johan W. van de Leur

Publication date: 20 May 2001

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4153/cjm-2001-012-4

zbMATH Keywords

nonlinear differential equationsGrassmann manifoldDarboux transformationKP hierarchy

Mathematics Subject Classification ID

Related Items (8)

Bilinear equations in Darboux transformations by boson-fermion correspondence ⋮ Cauchy problems related to integrable matrix hierarchies ⋮ The relative frame bundle of an infinite-dimensional flag variety and solutions of integrable hierarchies ⋮ A geometric construction of solutions of the strict \(\mathbf{h}\)-hierarchy ⋮ Darboux transformations for the strict KP hierarchy ⋮ Integrable hierarchies in the \(\mathbb{N} \times \mathbb{N}\)-matrices related to powers of the shift operator ⋮ Strict versions of integrable hierarchies in pseudodifference operators and the related Cauchy problems ⋮ Homogeneous spaces yielding solutions of the k[S –hierarchy and its strict version]

Cites Work

• Loop groups and equations of KdV type
• Geometrical interpretation of the bilinear equations of the KP hierarchy
• An analytic description of the vector constrained KP hierarchy
• Darboux theorems and Wronskian formulas for integrable systems. I: Constrained KP flows
• Birkhoff strata, Bäcklund transformations, and regularization of isospectral operators
• Wronskian solutions of the constrained Kadomtsev–Petviashvili hierarchy
• ASSOCIATED STURM-LIOUVILLE SYSTEMS
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