An \(r\)-matrix approach to nonstandard classes of integrable equations
From MaRDI portal
Publication:1318896
DOI10.2977/prims/1195166743zbMath0798.58037OpenAlexW2021030453MaRDI QIDQ1318896
B. G. Konopelchenko, Walter Oevel
Publication date: 1993
Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.2977/prims/1195166743
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) Pseudodifferential and Fourier integral operators on manifolds (58J40)
Related Items
Lie-algebraic structure of the Lax-integrable \((2|1 + 1)\)-dimensional supersymmetric matrix dynamical systems, Darboux theorems and Wronskian formulas for integrable systems. I: Constrained KP flows, Links between \((\gamma_n, \sigma_k)\)-KP hierarchy, \((\gamma_n, \sigma_k)\)-mKP hierarchy, and \((2+1)-(\gamma_n, \sigma_k)\)-Harry Dym hierarchy, A New Class of Soliton Solutions for the (Modified) Kadomtsev-Petviashvili Equation, Meromorphic Lax representations of (1+1)-dimensional multi-Hamiltonian dispersionless systems, On the modified KP hierarchy: tau functions, squared eigenfunction symmetries and additional symmetries, Hamiltonian structures of a coupled Ramani equation, Two new supersymmetric equations of harry dym type and their supersymmetric reciprocal transformations, On UrKdV and UrKP, Solving the constrained modified KP hierarchy by gauge transformations, On the nonlocal equations and nonlocal charges associated with the Harry Dym hierarchy, Squared eigenfunction symmetries for soliton equations. II, \({\mathcal R}\)-matrix approach to multi-Hamiltonian Lax dynamics, The Sato Grassmannian and the CH Hierarchy, A new 3-component Degasperis-Procesi hierarchy, R-matrix approach to lattice integrable systems, Symmetries and bilinear equations for the modified BKP hierarchy, A new generalized constrained modified KP hierarchy, Algebraic structure of the operator related to stationary systems, Modified constrained KP hierarchy and bi-Hamiltonian structures, Virasoro symmetry of constrained KP hierarchies, Recursion Operators for KP, mKP and Harry Dym Hierarchies, Multi-soliton solutions of a two-component Camassa–Holm system: Darboux transformation approach, Poisson algebras associated with constrained dispersionless modified Kadomtsev–Petviashvili hierarchies, On the dispersionless Dym hierarchy of hydrodynamic type: two approaches, On the Miura Map between the dispersionless KP and dispersionless modified KP hierarchies, Miura and auto-Bäcklund transformations for the cKP and cmKP hierarchies, Two-component coupled KdV equations and its connection with the generalized Harry Dym equations, On deformations of standard R-matrices for integrable infinite-dimensional systems, On the construction of recursion operator and algebra of symmetries for field and lattice systems, Rational solutions for a \((2+1)\)-dimensional nonlinear model in water waves generated by the Jaulent-Miodek hierarchy, Lie algebraic approach to the construction of (2+1)-dimensional lattice-field and field integrable Hamiltonian equations, Behaviors of \(N = 1\) supersymmetric Euler derivatives and Hamiltonian operators under general superconformal transformations, A Nonlinearly Dispersive Fifth Order Integrable Equation and its Hierarchy, Commutativity of the extended KP flows, Bilinear identities for the constrained modified KP hierarchy, Gauge equivalence and \(l\)-reductions of the differential-difference KP equation, Bi-Hamiltonian structures for integrable systems on regular time scales, Solutions of the constrained mKP hierarchy by Boson-Fermion correspondence, New extension of dispersionless Harry Dym hierarchy, The gauge transformation of the modified KP hierarchy, On the bi-Hamiltonian structure, dressing transformation and constrained flows for equations in \((2+1)\) dimensions, Supersymmetric reciprocal transformation and its applications, Integrable discrete systems on R and related dispersionless systems, Dispersionful analog of the Whitham hierarchy, Nonlocal integrable equations from the mKP hierarchy, Sato–Bäcklund transformations and string equations of the mKP hierarchy, Gauge Transformation and Reciprocal Link for (2+1)-Dimensional Integrable Field Systems, Constrained KP hierarchy and bi-Hamiltonian structures, Classical \(R\)-matrices on Poisson algebras and related dispersionless systems
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Integrable Hamiltonian systems connected with graded Lie algebras
- Solitons and infinite dimensional Lie algebras
- What is a classical r-matrix?
- Nonlinear Poisson structures and r-matrices
- Symplectic structures, their Bäcklund transformations and hereditary symmetries
- Algebraic aspects of nonlinear differential equations
- Modifying Lax equations and the second Hamiltonian structure
- 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
- Mathematics of dispersive water waves
- R-matrices and higher Poisson brackets for integrable systems
- A Method for Finding N-Soliton Solutions of the K.d.V. Equation and K.d.V.-Like Equation
- A Remark on the Commuting Flows Defined by Lax Equations
- The Painlevé property for partial differential equations. II: Bäcklund transformation, Lax pairs, and the Schwarzian derivative
- The Painlevé property for partial differential equations
- GAUGE TRANSFORMATIONS AND RECIPROCAL LINKS IN 2 + 1 DIMENSIONS
- On Reciprocal Bäcklund Transformations of Inverse Scattering Schemes
- Dressing transformations and Poisson group actions
- Solutions of the classical Yang-Baxter equation for simple Lie algebras
