The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
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Publication:3835072
DOI10.1063/1.528449zbMath0678.70015OpenAlexW2013673280MaRDI QIDQ3835072
Publication date: 1989
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1063/1.528449
trace identityisospectral problemssymplectic operatorhierarchy of evolution equationsHamiltonian structures of integrable systems
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)
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Cites Work
- Symplectic structures, their Bäcklund transformations and hereditary symmetries
- Canonical structure of soliton equations. I
- On formal variational calculus of higher dimensions
- Bäcklund transformations related to the Kaup-Newell spectral problem
- The Nonlinear Evolution Equations Related to the Wadati-Konno-Ichikawa Spectral Problem
- New Integrable Nonlinear Evolution Equations
- On a new hierarchy of Hamiltonian soliton equations
- Application of hereditary symmetries to nonlinear evolution equations
- On the Hamiltonian structure of evolution equations
- The modified Lax and two-dimensional Toda lattice equations associated with simple Lie algebras
- An exact solution for a derivative nonlinear Schrödinger equation
- A simple model of the integrable Hamiltonian equation
- Integrability of Nonlinear Hamiltonian Systems by Inverse Scattering Method
- The Recursion Operator of the Kadomtsev‐Petviashvili Equation and the Squared Eigenfunctions of the Schrödinger Operator
- On the Bäcklund transformation and Hamiltonian properties of superevaluation equations
- Korteweg-deVries Equation and Generalizations. V. Uniqueness and Nonexistence of Polynomial Conservation Laws