New integrable (3+1)-dimensional systems and contact geometry

Abstract

We introduce a novel systematic construction for integrable (3+1)-dimensional dispersionless systems using nonisospectral Lax pairs that involve contact vector fields. In particular, we present new large classes of (3+1)-dimensional integrable dispersionless systems associated to the Lax pairs which are polynomial and rational in the spectral parameter.

16 pages, LaTeX, no figures, revised and abridged, in this version (v5) the typos were fixed (including some that have unfortunately crept into the published version too), Letters in Mathematical Physics (2017)

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• Extended symmetry analysis of isothermal no-slip drift flux model
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• The Palatini star: exact solutions of the modified Lane-Emden equation
• Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model
• Integrable (3+1)-dimensional system with an algebraic Lax pair
• Generalized symmetries and conservation laws of (1+1)-dimensional Klein-Gordon equation
• Deforming Lie algebras to Frobenius integrable non-autonomous Hamiltonian systems
• Multidimensional integrable systems from contact geometry
• Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation
• Lie reductions and exact solutions of dispersionless Nizhnik equation
• Analysis of the symmetry group and exact solutions of the dispersionless KP equation in $n+1$ dimensions
• Lax pairs, recursion operators and bi-Hamiltonian representations of (3+1)-dimensional Hirota type equations
• Integrable (3+1)-dimensional generalization for dispersionless Davey--Stewartson system
• Contact Lie systems on Riemannian and Lorentzian spaces: from scaling symmetries to curvature-dependent reductions
• From the conformal self-duality equations to the Manakov-Santini system
• Integrability of anti-self-dual vacuum Einstein equations with nonzero cosmological constant: an infinite hierarchy of nonlocal conservation laws