On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations
We studied, for the Kortweg–de Vries–Burgers equations on cylindrical and spherical waves, the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary. The regular profile at the vicinity of perturbation looks like a periodical chain of shock front...
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MDPI AG
2021-01-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/2/220 |
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doaj-f25a4a1801134346bef6a832f967d0942021-01-30T00:00:16ZengMDPI AGSymmetry2073-89942021-01-011322022010.3390/sym13020220On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers EquationsAlexey Samokhin0Trapeznikov Institute of Control Scienties, Russian Academy of Sciences, 65 Profsoyuznaya Street, 117997 Moscow, RussiaWe studied, for the Kortweg–de Vries–Burgers equations on cylindrical and spherical waves, the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary. The regular profile at the vicinity of perturbation looks like a periodical chain of shock fronts with decreasing amplitudes. Further on, shock fronts become decaying smooth quasi-periodic oscillations. After the oscillations cease, the wave develops as a monotonic convex wave, terminated by a head shock of a constant height and equal velocity. This velocity depends on integral characteristics of a boundary condition and on spatial dimensions. In this paper the explicit asymptotic formulas for the monotonic part, the head shock and a median of the oscillating part are found.https://www.mdpi.com/2073-8994/13/2/220Korteweg–de Vries–Burgers equationcylindrical and spherical wavessaw-tooth solutionsperiodic boundary conditionshead shock wave |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Alexey Samokhin |
| spellingShingle |
Alexey Samokhin On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations Symmetry Korteweg–de Vries–Burgers equation cylindrical and spherical waves saw-tooth solutions periodic boundary conditions head shock wave |
| author_facet |
Alexey Samokhin |
| author_sort |
Alexey Samokhin |
| title |
On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations |
| title_short |
On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations |
| title_full |
On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations |
| title_fullStr |
On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations |
| title_full_unstemmed |
On Monotonic Pattern in Periodic Boundary Solutions of Cylindrical and Spherical Kortweg–De Vries–Burgers Equations |
| title_sort |
on monotonic pattern in periodic boundary solutions of cylindrical and spherical kortweg–de vries–burgers equations |
| publisher |
MDPI AG |
| series |
Symmetry |
| issn |
2073-8994 |
| publishDate |
2021-01-01 |
| description |
We studied, for the Kortweg–de Vries–Burgers equations on cylindrical and spherical waves, the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary. The regular profile at the vicinity of perturbation looks like a periodical chain of shock fronts with decreasing amplitudes. Further on, shock fronts become decaying smooth quasi-periodic oscillations. After the oscillations cease, the wave develops as a monotonic convex wave, terminated by a head shock of a constant height and equal velocity. This velocity depends on integral characteristics of a boundary condition and on spatial dimensions. In this paper the explicit asymptotic formulas for the monotonic part, the head shock and a median of the oscillating part are found. |
| topic |
Korteweg–de Vries–Burgers equation cylindrical and spherical waves saw-tooth solutions periodic boundary conditions head shock wave |
| url |
https://www.mdpi.com/2073-8994/13/2/220 |
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