Classification of integrable hydrodynamic chains

2010/01/31 by A. V. Odesskiĭ, A. Odesskii, В. В. Соколов +1 · 7 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Chain (unit) #Class (philosophy) #Computer science #Geology #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Physics #Pure mathematics #Quantum mechanics #Type (biology) #math.AP #nlin.SI

paper · pdf · doi:10.1088/1751-8113/43/43/434027

published in Journal of Physics A Mathematical and Theoretical 43(43), 434027 (Institute of Physics) · 20 pages, latex

arxiv created 2010/03/03 · openalex publication_date 2010/10/12 · arxiv updated 2015/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Using the method of hydrodynamic reductions, we find all integrable infinite (1+1)-dimensional hydrodynamic-type chains of shift one. A class of integrable infinite (2+1)-dimensional hydrodynamic-type chains is constructed.

Citations

• Systems of Gibbons-Tsarev type and integrable 3-dimensional models
• Integrable pseudopotentials related to elliptic curves
• Classification of integrable hydrodynamic chains and generating functions of conservation laws
• Integrable pseudopotentials related to generalized hypergeometric functions

Cited by

• Random matrix ensembles and integrable differential identities