A hierarchy of integrable partial differential equations in \(2+1\) dimensions associated with one-parameter families of one-dimensional vector fields

DOI10.1007/s11232-007-0084-2zbMath1131.37061OpenAlexW2091626814MaRDI QIDQ2461078

S. V. Manakov, Paolo Maria Santíni

Publication date: 21 November 2007

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

Full work available at URL: https://doi.org/10.1007/s11232-007-0084-2

zbMATH Keywords

inverse scattering transformintegrable systemnonlinear Riemann problem

Mathematics Subject Classification ID

Related Items (23)

A simple construction of recursion operators for multidimensional dispersionless integrable systems ⋮ The Cauchy problem for the Pavlov equation ⋮ Wave breaking in solutions of the dispersionless Kadomtsev-Petviashvili equation at a finite time ⋮ Matrix extension of the Manakov-Santini system and an integrable chiral model on an Einstein-Weyl background ⋮ Lie symmetries, group classification and conserved quantities of dispersionless Manakov-Santini system in \((2+1)\)-dimension ⋮ Frobenius manifold for the dispersionless Kadomtsev-Petviashvili equation ⋮ Dispersionless integrable systems and the Bogomolny equations on an Einstein-Weyl geometry background ⋮ Numerical study of shock formation in the dispersionless Kadomtsev-Petviashvili equation and dispersive regularizations ⋮ An integral geometry lemma and its applications: the nonlocality of the Pavlov equation and a tomographic problem with opaque parabolic objects ⋮ A note on the hyper-CR equation, and gauged \(N=2\) supergravity ⋮ On an integrable multi-dimensionally consistent 2 n  + 2 n -dimensional heavenly-type equation ⋮ The Cauchy problem for the Pavlov equation with large data ⋮ On linear degeneracy of integrable quasilinear systems in higher dimensions ⋮ Nonlinear nonisospectral differential coverings for the hyper-CR equation of Einstein-Weyl structures and the Gibbons-Tsarev equation ⋮ Integrable \((2+1)\)-dimensional systems of hydrodynamic type ⋮ On the relationship between nonlinear equations integrable by the method of characteristics and equations associated with commuting vector fields ⋮ Coverings over Lax integrable equations and their nonlocal symmetries ⋮ Nonlocality and the Inverse Scattering Transform for the Pavlov Equation ⋮ A class of multidimensional integrable hierarchies and their reductions ⋮ Hodograph solutions for the Manakov–Santini equation ⋮ Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions ⋮ SDYM equations on the self-dual background ⋮ Hierarchies of Manakov-Santini type by means of Rota-Baxter and other identities

Cites Work

• A class of Einstein-Weyl spaces associated to an integrable system of hydrodynamic type
• Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation
• The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Recursion operators and bi-Hamiltonian structures in multidimensions. I
• On the integrability of \((2+1)\)-dimensional quasilinear systems
• A simple model of the integrable Hamiltonian equation
• The τ‐function of the universal whitham hierarchy, matrix models and topological field theories
• On twistor solutions of the dKP equation
• The $\bar{\partial}$-approach to the dispersionless KP hierarchy
• Integrable hydrodynamic chains
• INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT
• Einstein-Weyl geometry, the dKP equation and twistor theory
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