Geodesic
Travelling wave solutions to two-velocity deep bed filtration equations
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2023), pp. 65-70

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Travelling wave solutions to the deep bed filtration system are constructed for a model with different velocities of a carrier fluid and suspended particles. The solution in quadratures is obtained when the velocity of the carrier fluid and that of the particles differ by a concentration-dependent factor. For some special cases, the physically realizable domains are found in the space of governing parameters. Solutions that may be interpreted as a clogging wave structure are presented. 
@article{VMUMM_2023_6_a10,
     author = {N. E. Leont'ev and K. Taurbayeva},
     title = {Travelling wave solutions to two-velocity deep bed filtration equations},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {65--70},
     publisher = {mathdoc},
     number = {6},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_6_a10/}
}
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N. E. Leont'ev; K. Taurbayeva. Travelling wave solutions to two-velocity deep bed filtration equations. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2023), pp. 65-70. http://geodesic.mathdoc.fr/item/VMUMM_2023_6_a10/