https://doi.org/10.1140/epjp/s13360-020-00659-3
Regular Article
Traveling waves and undercompressive shocks in solutions of the generalized Korteweg–de Vries–Burgers equation with a time-dependent dissipation coefficient distribution
1
Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina St., 119991, Moscow, Russia
2
National Research Nuclear University “MePHI”, Kashirskoye shosse 31, 115409, Moscow, Russia
3
N. N. Semenov Institute of Chemical Physics (ICP), Russian Academy of Sciences, Moscow, Russia
a
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Received:
21
April
2020
Accepted:
30
July
2020
Published online:
7
August
2020
Abstract
Solutions of the generalized KdV–Burgers equation are analyzed in the case when the dissipation coefficient depends on the spatial coordinate and time. Solutions in the form of traveling waves describing the structure of discontinuities, including special discontinuities, are studied. In the frame of this problem, nonstationary solutions of the generalized KdV–Burgers equation including the special discontinuity are numerically found.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
