Geodesic
Reflection and refraction of solitons by the~$\text{KdV}$--Burgers equation in nonhomogeneous dissipative media
Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 1, pp. 153-160

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We study the behavior of the soliton that encounters a barrier with dissipation while moving in a nondissipative medium. We use the Korteweg–de Vries–Burgers equation to model this situation. The modeling includes the case of a finite dissipative layer similar to a wave passing through air–glass–air and also a wave passing from a nondissipative layer into a dissipative layer (similar to light passing from air to water). The dissipation predictably reduces the soliton amplitude/velocity. Other effects also occur in the case of a finite barrier in the soliton path: after the wave leaves the dissipative barrier, it retains the soliton form, but a reflection wave arises as small and quasiharmonic oscillations (a breather). The breather propagates faster than the soliton passing through the barrier.
Keywords: KdV–Burgers equation, nonhomogeneous layered media, reflection, refraction.
Mots-clés : soliton 
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     author = {A. V. Samokhin},
     title = {Reflection and refraction of solitons by the~$\text{KdV}${--Burgers} equation in nonhomogeneous dissipative media},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {153--160},
     publisher = {mathdoc},
     volume = {197},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2018_197_1_a8/}
}
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A. V. Samokhin. Reflection and refraction of solitons by the~$\text{KdV}$--Burgers equation in nonhomogeneous dissipative media. Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 1, pp. 153-160. http://geodesic.mathdoc.fr/item/TMF_2018_197_1_a8/