Geodesic
Integrability of exceptional hydrodynamic-type systems
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Topology and physics, Tome 302 (2018), pp. 343-353

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We consider non-diagonalizable hydrodynamic-type systems integrable by the extended hodograph method. We restrict the analysis to non-diagonalizable hydrodynamic reductions of the three-dimensional Mikhalev equation. We show that families of these hydrodynamic-type systems are reducible to the heat hierarchy. Then we construct new particular explicit solutions for the Mikhalev equation.
Keywords: integrable quasilinear systems of first order, linearly degenerate systems of first order, characteristic velocities, extended hodograph method. 
@article{TM_2018_302_a16,
     author = {Maxim V. Pavlov},
     title = {Integrability of exceptional hydrodynamic-type systems},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {343--353},
     publisher = {mathdoc},
     volume = {302},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2018_302_a16/}
}
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Maxim V. Pavlov. Integrability of exceptional hydrodynamic-type systems. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Topology and physics, Tome 302 (2018), pp. 343-353. http://geodesic.mathdoc.fr/item/TM_2018_302_a16/