Geodesic
On the model of $z$-pinch instability
Matematičeskoe modelirovanie, Tome 10 (1998) no. 12, pp. 87-95 
A. I. Lobanov. On the model of $z$-pinch instability. Matematičeskoe modelirovanie, Tome 10 (1998) no. 12, pp. 87-95. http://geodesic.mathdoc.fr/item/MM_1998_10_12_a2/
@article{MM_1998_10_12_a2,
     author = {A. I. Lobanov},
     title = {On the model of $z$-pinch instability},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {87--95},
     year = {1998},
     volume = {10},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_1998_10_12_a2/}
}
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The mathematical model of $z$-pinch's faist high-frequency instability evolution is considered as a system of small additions into self-similar one-dimension solution. Additions behavior about initial moment is analyzed. Qualitative comparison with the results of numerical researches of one-fluid one-temperature MHD model is carried out.