GALILEAN SYMMETRY INVARIANT SOLUTIONS TO THE KDV-BURGERS EQUATION AND NONLINEAR SUPERPOSITION OF SHOCK WAVES
A description of the Galilean symmetry invariant solutions to the KdV-Burgers equation is reduced to studying of phase trajectories of the corresponding ODE depending on a parameter (the velocity of a shock wave propagation). Exact invariant solutions are simple shock waves that become separatrixes...
| Main Authors: | , |
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| Format: | Article |
| Language: | Russian |
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Moscow State Technical University of Civil Aviation
2016-12-01
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| Series: | Научный вестник МГТУ ГА |
| Subjects: | |
| Online Access: | https://avia.mstuca.ru/jour/article/view/850 |
| Summary: | A description of the Galilean symmetry invariant solutions to the KdV-Burgers equation is reduced to studying of phase trajectories of the corresponding ODE depending on a parameter (the velocity of a shock wave propagation). Exact invariant solutions are simple shock waves that become separatrixes on the phase portrait which always has two singular points for a given value of the parameter. For nonlinear superposition of shock waves the phase portrait contains four singular points; its consequent bifurcations lead to oscillations. |
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| ISSN: | 2079-0619 2542-0119 |