Abstract
In this paper, we introduce a new property of two-dimensional integrable hydrodynamic chains—existence of infinitely many local three-dimensional conservation laws for pairs of integrable two-dimensional commuting flows. Infinitely many local three-dimensional conservation laws for the Benney commuting hydrodynamic chains are constructed. As a by-product, we established a new method for computation of local conservation laws for three-dimensional integrable systems. The Mikhalëv equation and the dispersionless limit of the Kadomtsev-Petviashvili equation are investigated. All known local and infinitely many new quasilocal three-dimensional conservation laws are presented. Also four-dimensional conservation laws are considered for couples of three-dimensional integrable quasilinear systems and for triplets of corresponding hydrodynamic chains.
| Original language | English |
|---|---|
| Pages (from-to) | 339-355 |
| Number of pages | 17 |
| Journal | Studies in Applied Mathematics |
| Volume | 143 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Nov 2019 |
Keywords
- dispersionless limit of the Kadomtsev-Petviashvili equation
- integrable system
- multi-dimensional conservation laws
- the Benney hydrodynamic chain
- then Mikhalëv equation
- GEOMETRIC APPROACH
- WAVES
- EQUATIONS
- then Mikhalev equation