Journal
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
Volume 58, Issue 4, Pages 535-570Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/s00033-006-6076-5
Keywords
solitary waves; KdV equations
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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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