Geodesic
The influence of the viscosity on the structure of the MKdV shock waves
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 11, Tome 199 (1992), pp. 37-42

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We consider shock problem for “non-selfadjoint” MKdV integrable model. It is shown that this problem is stable and the long-time asymptotics of the solution is obtained. Non-conservative perturbation of this problem is discussed. 
@article{ZNSL_1992_199_a2,
     author = {R. F. Bikbaev},
     title = {The influence of the viscosity on the structure of the {MKdV} shock waves},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {37--42},
     publisher = {mathdoc},
     volume = {199},
     year = {1992},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1992_199_a2/}
}
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R. F. Bikbaev. The influence of the viscosity on the structure of the MKdV shock waves. Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics. Part 11, Tome 199 (1992), pp. 37-42. http://geodesic.mathdoc.fr/item/ZNSL_1992_199_a2/