Geodesic
Integrable hydrodynamic submodels with a~linear velocity field
Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 3, pp. 135-145

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Invariant and partially invariant solutions to equations of gas dynamics with a linear velocity field are given by a matrix satisfying a homogeneous integrable Riccati equation. The classification of solutions by the acceleration vector in the Lagrangian coordinates is carried out. We give an example of an invariant solution for which the selected volume “collapses” to an interval.
Keywords: gas dynamics equations, state equation, intregrable submodels with linear velocity field. 
@article{SJIM_2012_15_3_a12,
     author = {L. Z. Urazbakhtina},
     title = {Integrable hydrodynamic submodels with a~linear velocity field},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {135--145},
     publisher = {mathdoc},
     volume = {15},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2012_15_3_a12/}
}
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L. Z. Urazbakhtina. Integrable hydrodynamic submodels with a~linear velocity field. Sibirskij žurnal industrialʹnoj matematiki, Tome 15 (2012) no. 3, pp. 135-145. http://geodesic.mathdoc.fr/item/SJIM_2012_15_3_a12/