Geodesic
Shock waves in one-dimensional models with cubic nonlinearity
Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 2, pp. 191-212

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Shock waves are described qualitatively for a class of one-dimensional models with cubic nonlinearity (of the type of the modified Korteweg–de Vries equation): $u_t-6u^2u_x+\gamma u_{xxx}=\nu u_{xx}$. Both the integrable and the nonintegrable case are considered. The behavior of a shock wave in the limit $t \to \infty$ is considered. 
@article{TMF_1993_97_2_a2,
     author = {R. F. Bikbaev},
     title = {Shock waves in one-dimensional models with cubic nonlinearity},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {191--212},
     publisher = {mathdoc},
     volume = {97},
     number = {2},
     year = {1993},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_97_2_a2/}
}
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R. F. Bikbaev. Shock waves in one-dimensional models with cubic nonlinearity. Teoretičeskaâ i matematičeskaâ fizika, Tome 97 (1993) no. 2, pp. 191-212. http://geodesic.mathdoc.fr/item/TMF_1993_97_2_a2/