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

This article is cited in 3 scientific papers (total in 3 papers)

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

Full text: PDF file (527 kB)
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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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\by A.~V.~Samokhin
\paper Reflection and refraction of solitons by the~$\text{KdV}$--Burgers equation in nonhomogeneous dissipative media
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\pages 1527--1533
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  • https://doi.org/10.4213/tmf9474
  • http://mi.mathnet.ru/eng/tmf/v197/i1/p153

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. P. Chugainova, V. A. Shargatov, “Traveling waves and undercompressive shocks in solutions of the generalized Korteweg-de Vries-Burgers equation with a time-dependent dissipation coefficient distribution”, Eur. Phys. J. Plus, 135:8 (2020), 635  crossref  isi
    2. A. Samokhin, “Soliton transmutations in KdV-Burgers layered media”, J. Geom. Phys., 148 (2020), 103547  crossref  mathscinet  zmath  isi
    3. A. Samokhin, “On connection between the splitting parameters of KdV initial datum and its conserved quantities”, Lobachevskii J. Math., 41:12, SI (2020), 2482–2490  crossref  zmath  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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