Non-diagonalisable Hydrodynamic Type Systems, Integrable by Tsarev's Generalised Hodograph Method

Abstract: We present a wide class of non-diagonalizable hydrodynamic type systems, which can be integrated by Tsarev's generalized hodograph method. This class of hydrodynamic type systems contains Jordan blocks 2x2 only. The Haantjes tensor has vanished. This means such 2N component hydrodynamic type systems possess N Riemann invariants and N double eigenvalues only.

First multi-component example was extracted from El's nonlocal kinetic equation, describing dense soliton gas. All conservation laws and commuting flows were found. A general solution is constructed.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic

Mathematical models and integration methods