Seminar talk, 30 March 2016

From Geometry of Differential Equations
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Speaker: Alexey Samokhin

Title: On nonlinear superposition of shock waves for the Korteweg-de Vries-Burgers equation

Nonlinear superposition of analytically given monotone shock waves, which are Galilean invariant solutions of the Korteweg-de Vries-Burgers equation, are studied and numerically modeled. The initial profile of the form of the sum of shock waves with time gradually transform itself to a more complicated Galilean invariant solution. We trace the stages of transformation of the phase portrait and the character of singular points of the accompanying dynamical system.