Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation

DOI10.1016/j.physleta.2006.07.011zbMath1236.37042arXivnlin/0604024OpenAlexW1979703466MaRDI QIDQ942596

Publication date: 5 September 2008

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0604024

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) PDEs in connection with relativity and gravitational theory (35Q75) Asymptotic procedures (radiation, news functions, (mathcal{H} )-spaces, etc.) in general relativity and gravitational theory (83C30) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items

A simple construction of recursion operators for multidimensional dispersionless integrable systems, A cohomological approach to immersed submanifolds via integrable systems, On a class of integrable systems of Monge-Ampère type, Six-dimensional heavenly equation. Dressing scheme and the hierarchy, The Cauchy problem for the Pavlov equation, On integration of a multidimensional version of n-wave type equation, Non-homogeneous systems of hydrodynamic type possessing Lax representations, Lie-algebraic structure of Lax-Sato integrable heavenly equations and the Lagrange-d'Alembert principle, Wave breaking in solutions of the dispersionless Kadomtsev-Petviashvili equation at a finite time, Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. II, Lax representations with non-removable parameters and integrable hierarchies of PDEs via exotic cohomology of symmetry algebras, Lie symmetries, group classification and conserved quantities of dispersionless Manakov-Santini system in \((2+1)\)-dimension, Five-dimensional Lax-integrable equation, its reductions and recursion operator, Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. I, Linearly degenerate hierarchies of quasiclassical SDYM type, A hierarchy of integrable partial differential equations in \(2+1\) dimensions associated with one-parameter families of one-dimensional vector fields, Duality of positive and negative integrable hierarchies via relativistically invariant fields, Whitham modulation theory for the Kadomtsev– Petviashvili equation, The Lax-Sato integrable heavenly equations on functional supermanifolds and their Lie-algebraic structure, An integral geometry lemma and its applications: the nonlocality of the Pavlov equation and a tomographic problem with opaque parabolic objects, On an integrable multi-dimensionally consistent 2 n + 2 n -dimensional heavenly-type equation, Second-order PDEs in four dimensions with half-flat conformal structure, Self-dual Einstein spaces and the general heavenly equation. Eigenfunctions as coordinates, The Cauchy problem for the Pavlov equation with large data, On linear degeneracy of integrable quasilinear systems in higher dimensions, A modification of the method of characteristics: a new class of multidimensional partially integrable nonlinear systems, Type II hidden symmetries of the second heavenly equation, Integrable \((2+1)\)-dimensional systems of hydrodynamic type, On the integrability of symplectic Monge-Ampère equations, On the relationship between nonlinear equations integrable by the method of characteristics and equations associated with commuting vector fields, On \((2+1)\)-dimensional hydrodynamic type systems possessing a pseudopotential with movable singularities, Lie symmetry reductions and group invariant solutions of \((2+1)\)-dimensional modified Veronese web equation, On the dispersionless Davey-Stewartson system: Hamiltonian vector field Lax pair and relevant nonlinear Riemann-Hilbert problem for dDS-II system, Nonlocality and the Inverse Scattering Transform for the Pavlov Equation, Characteristic integrals in 3D and linear degeneracy, Lagrangian extensions of multi-dimensional integrable equations. I: The five-dimensional Martínez Alonso-Shabat equation, Hierarchies of Manakov-Santini type by means of Rota-Baxter and other identities

Cites Work