Solitary waves and their linear stability in weakly coupled KdV equations |
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Authors: | J Douglas Wright and Arnd Scheel |
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Institution: | (2) Department of Mathematics, University of Texas – Pan American, Edinburg, USA; |
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Abstract: | We consider a system of weakly coupled KdV equations developed initially by Gear & Grimshaw to model interactions between
long waves. We prove the existence of a variety of solitary wave solutions, some of which are not constrained minimizers.
We show that such solutions are always linearly unstable. Moreover, the nature of the instability may be oscillatory and as
such provides a rigorous justification for the numerically observed phenomenon of “leapfrogging.” |
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