Hamiltonian structure of Sato's hierarchy of KP equations and a coadjoint orbit of a certain formal Lie group

DOI10.1007/BF00419926zbMath0584.58021OpenAlexW2014390173WikidataQ115395006 ScholiaQ115395006MaRDI QIDQ1069524

Yoshihide Watanabe

Publication date: 1983

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00419926

zbMATH Keywords

Kadomtsev-Petviashvili equationscompletely integrable Hamiltonian systemsKostant-Kirillov coadjoint orbit

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Initial value problems for linear higher-order PDEs (35G10) Higher-order parabolic equations (35K25)

Related Items (14)

Canonical property of the Miura maps between the MKP and KP hierarchies, continuous and discrete ⋮ Maslov-Poisson measure and Feynman formulas for the solution of the Dirac equation ⋮ Integrability of the Frobenius algebra-valued Kadomtsev-Petviashvili hierarchy ⋮ Free-field realization of the \(W_{KP}^{(N)}\) algebra ⋮ A new scheme of integrability for (bi)Hamiltonian PDE ⋮ Remarks on Hamiltonian structures of the KP hierarchy and \(W_{\text{KP}}^{(q)}\) algebra ⋮ On diff(S1) covariantization of pseudodifferential operator ⋮ The higher order Hamiltonian structures for the modified classical Yang-Baxter equation ⋮ Hamiltonian structures of the constrained \(\mathfrak{F}\)-valued KP hierarchy ⋮ Well-posedness of the Kadomtsev-Petviashvili hierarchy, Mulase factorization, and Frölicher Lie groups ⋮ A gauge theory of the Kadomtsev-Petviashvili system ⋮ The spectrum for solutions of the modified classical Yang-Baxter equation and algebraic groups. ⋮ A one-parameter family of Hamiltonian structures for the KP hierarchy and a continuous deformation of the nonlinear \(W_{\text{KP}}\) algebra ⋮ Hamiltonian structure of Kadomtsev-Petviashvili type equations

Cites Work

• Hamiltonian structure of M. Sato's hierarchy of Kadomtsev-Petviashvili equation
• Algebraic aspects of nonlinear differential equations
• Gel'fand-Dikii Hamiltonian operator and the coadjoint representation of the Volterra group
• Fractional powers of operators and Hamiltonian systems
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations

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