Geodesic
Stability of a traveling-wave solution of the Cauchy problem for the Korteweg–de Vries–Burgers equation
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 4, pp. 725-745

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The asymptotic behavior of the solution to the Cauchy problem for the Korteweg–de Vries–Burgers equation $u_t+(f(u))_x+au_{xxx}-bu_{xx}=0$ as $t\to\infty$ is analyzed. Sufficient conditions for the existence and local stability of a traveling-wave solution known in the case of $f(u)=u^2$ are extended to the case of an arbitrary sufficiently smooth convex function $f(u)$. 
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     author = {A. V. Kazeǐkina},
     title = {Stability of a traveling-wave solution of the {Cauchy} problem for the {Korteweg{\textendash}de} {Vries{\textendash}Burgers} equation},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {725--745},
     publisher = {mathdoc},
     volume = {50},
     number = {4},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_4_a10/}
}
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A. V. Kazeǐkina. Stability of a traveling-wave solution of the Cauchy problem for the Korteweg–de Vries–Burgers equation. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 4, pp. 725-745. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_4_a10/