Integrable deformations in the algebra of pseudodifferential operators from a Lie algebraic perspective

DOI10.1007/s11232-013-0011-7zbMath1352.17030OpenAlexW2012477639WikidataQ57429133 ScholiaQ57429133MaRDI QIDQ394906

Elena A. Panasenko, Aloysius G. Helminck, Gerardus F. Helminck

Publication date: 28 January 2014

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11232-013-0011-7

zbMATH Keywords

linearizationpseudodifferential operatorLax equationintegrable deformationKadomtsev-Petviashvili hierarchyzero-curvature relation

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Applications of Lie algebras and superalgebras to integrable systems (17B80)

Related Items (16)

Bilinear equations for the strict KP hierarchy ⋮ A geometric construction of solutions of the strict \(\mathrm{dKP}(\Lambda_0)\) hierarchy ⋮ Minimal realizations of the KP hierarchy, its strict version and their reductions ⋮ Reductions of the strict KP hierarchy ⋮ The strict AKNS hierarchy: its structure and solutions ⋮ Integrable deformations in the matrix pseudo differential operators ⋮ An integrable hierarchy including the AKNS hierarchy and its strict version ⋮ Expressions in Fredholm determinants for solutions of the strict KP hierarchy ⋮ Darboux transformations for the strict KP hierarchy ⋮ Infinite dimensional symmetric spaces and Lax equations compatible with the infinite Toda chain ⋮ Cauchy problems related to integrable deformations of pseudo differential operators ⋮ Integrable hierarchies in the \(\mathbb{N} \times \mathbb{N}\)-matrices related to powers of the shift operator ⋮ Geometric solutions of the strict KP hierarchy ⋮ Strict versions of integrable hierarchies in pseudodifference operators and the related Cauchy problems ⋮ Properties of the algebra Psd related to integrable hierarchies ⋮ Scaling invariance of the strict KP hierarchy

Cites Work

• Complete integrability of the Kadomtsev-Petviashvili equation
• Loop groups and equations of KdV type
• The solution to a generalized Toda lattice and representation theory
• SPACES OF BOUNDARY VALUES RELATED TO A MULTIPOINT VERSION OF THE KP-HIERARCHY
• Integrals of nonlinear equations of evolution and solitary waves
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