GALILEAN SYMMETRY INVARIANT SOLUTIONS TO THE KDV-BURGERS EQUATION AND NONLINEAR SUPERPOSITION OF SHOCK WAVES
Abstract
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.
About the Authors
Y. I. Dementyev
МГТУ ГА
Russian Federation
Russian Federation
A. V. Samokhin
МГТУ ГА
Russian Federation
Russian Federation
References
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Review
For citations:
Dementyev Y.I., Samokhin A.V. GALILEAN SYMMETRY INVARIANT SOLUTIONS TO THE KDV-BURGERS EQUATION AND NONLINEAR SUPERPOSITION OF SHOCK WAVES. Civil Aviation High Technologies. 2016;(224):24-32. (In Russ.)
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