Geodesic
Spectral stability theory of heteroclinic solutions to the Korteweg--de Vries--Burgers equation with an arbitrary potential
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 295 (2016), pp. 163-173

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The analysis of stability of heteroclinic solutions to the Korteweg–de Vries–Burgers equation is generalized to the case of an arbitrary potential that gives rise to heteroclinic states. An example of a specific nonconvex potential is given for which there exists a wide set of heteroclinic solutions of different types. Stability of the corresponding solutions in the context of uniqueness of a solution to the problem of decay of an arbitrary discontinuity is discussed. 
@article{TM_2016_295_a7,
     author = {A. T. Il'ichev and A. P. Chugainova},
     title = {Spectral stability theory of heteroclinic solutions to the {Korteweg--de} {Vries--Burgers} equation with an arbitrary potential},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {163--173},
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     volume = {295},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2016_295_a7/}
}
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A. T. Il'ichev; A. P. Chugainova. Spectral stability theory of heteroclinic solutions to the Korteweg--de Vries--Burgers equation with an arbitrary potential. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mechanics, Tome 295 (2016), pp. 163-173. http://geodesic.mathdoc.fr/item/TM_2016_295_a7/