Towards a theory of differential constraints of a hydrodynamic hierarchy
arXiv:nlin/0310036 · doi:10.2991/jnmp.2003.10.2.6
Abstract
We present a theory of compatible differential constraints of a hydrodynamic hierarchy of infinite-dimensional systems. It provides a convenient point of view for studying and formulating integrability properties and it reveals some hidden structures of the theory of integrable systems. Illustrative examples and new integrable models are exhibited.
Published by JNMP at http://www.sm.luth.se/math/JNMP/
Cited by in corpus (27)
- A class of Einstein--Weyl spaces associated to an integrable system of hydrodynamic type
- Hydrodynamic reductions of multi-dimensional dispersionless PDEs: the test for integrability
- Interpolating Dispersionless Integrable System
- Multi-component generalizations of the {CH} equation: Geometrical Aspects, Peakons and Numerical Examples
- Looped cotangent Virasoro algebra and non-linear integrable systems in dimension 2+1
- On the solutions of the second heavenly and Pavlov equations
- On the dbar-dressing method applicable to heavenly equation
- Classical R-matrix theory for bi-Hamiltonian field systems
- The Inverse Spectral Transform for the Dunajski hierarchy and some of its reductions, I: Cauchy problem and longtime behavior of solutions
- The dispersionless 2D Toda equation: dressing, Cauchy problem, longtime behavior, implicit solutions and wave breaking
- Central extensions of cotangent universal hierarchy: (2+1)-dimensional bi-Hamiltonian systems
- Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking
- Integrable Dispersive Chains and Energy Dependent Schrodinger Operator
- Integrable dispersionless PDEs arising as commutation condition of pairs of vector fields
- Integrability of the Manakov--Santini hierarchy
- Parabolic regularization of the gradient catastrophes for the Burgers-Hopf equation and Jordan chain
- From Stäckel systems to integrable hierarchies of PDE's: Benenti class of separation relations
- Hierarchies of Manakov-Santini Type by Means of Rota-Baxter and Other Identities
- Multidimensional integrable systems and deformations of Lie algebra homomorphisms
- A dispersionless integrable system associated to Diff gauge theory
- On deformations of the dispersionless Hirota equation
- Classification of integrable Hamiltonian hydrodynamic chains associated with Kupershmidt's brackets
- Differential-geometric approach to the integrability of hydrodynamic chains: the Haantjes tensor
- The Cauchy problem for the Pavlov equation
- Integrable Dispersive Chains and Their Multi-Phase Solutions
- From the conformal self-duality equations to the Manakov-Santini system
- A new class of linearizable equations