Examples of the absence of a traveling wave for the generalized Korteweg-de Vries-Burgers equation
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An example of convex function f(u) for which the generalized Korteweg-de Vries-Burgers equation u t + (f(u)) x + au xxx − bu xx = 0 has no solutions in the form of a traveling wave with specified limits at infinity is constructed. This example demonstrates the difficulties in analyzing asymptotic behavior of the Cauchy problem for the Korteweg-de Vries-Burgers equation that is not inherent in the type of equation for the conservation law, the Burgers-type equation, and its finite difference analog.
KeywordsKorteweg-de Vries-Burgers equation traveling wave
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