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TMF, 2018, Volume 197, Number 1, Pages 153–160 (Mi tmf9474)  

Reflection and refraction of solitons by the $KdV$–Burgers equation in nonhomogeneous dissipative media

A. V. Samokhinab

a Trapeznikov Institute of Control Sciences, RAS, Moscow, Russia
b Moscow State Technical University of Civil Aviation, Moscow, Russia

Abstract: 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, soliton, reflection, refraction.

DOI: https://doi.org/10.4213/tmf9474

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English version:
Theoretical and Mathematical Physics, 2018, 197:1, 1527–1533

Bibliographic databases:

PACS: 03.65.Ge (PACS2010)
MSC: 35Q51 (MSC2010)
Received: 30.09.2017

Citation: A. V. Samokhin, “Reflection and refraction of solitons by the $KdV$–Burgers equation in nonhomogeneous dissipative media”, TMF, 197:1 (2018), 153–160; Theoret. and Math. Phys., 197:1 (2018), 1527–1533

Citation in format AMSBIB
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