Systems of Gibbons-Tsarev type and integrable 3-dimensional models

2009/06/18 by A. V. Odesskiĭ, A. V. Odesskii, В. В. Соколов +3 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #hep-th #math.AG #math.AP #nlin.SI

paper · pdf · doi:10.48550/arxiv.0906.3509

18 pages, latex

arxiv created 2009/06/18 · openalex publication_date 2009/06/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We review the role of Gibbons-Tsarev-type systems in classification of integrable multi-dimensional hydrodynamic-type systems. Our main observation is an universality of Gibbons-Tsarev-type systems. We also constract explicitly a wide class of 3-dimensional hydrodynamic-type systems corresponding to the simplest possible Gibbons-Tsarev-type system.

Citations

• Integrable pseudopotentials related to elliptic curves

Cited by

• On linear degeneracy of integrable quasilinear systems in higher dimensions
• Integrability properties of some symmetry reductions

Related

• Integrability of the Gibbons--Tsarev system
• On (2+1)-dimensional hydrodynamic type systems possessing pseudopotential with movable singularities
• Integrability of the Manakov--Santini hierarchy
• Lagrangian multiforms and dispersionless integrable systems
• A family of (2+1)-dimensional hydrodynamic type systems possessing pseudopotential