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Instability of a class of dispersive solitary waves*

Published online by Cambridge University Press:  14 November 2011

P. E. Souganidis  and
W. A. Strauss
P. E. Souganidis
Affiliation:
Division of Applied Mathematics, Department of Mathematics, and Lefschetz Center for Dynamical Systems, Brown University, Providence, RI02912, U.S.A.
W. A. Strauss
Affiliation:
Division of Applied Mathematics, Department of Mathematics, and Lefschetz Center for Dynamical Systems, Brown University, Providence, RI02912, U.S.A.
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Synopsis

This paper studies the stability and instability properties of solitary wave solutions φ(x – ct) of a general class of evolution equations of the form Muttf(u)x=0, which support weakly nonlinear dispersive waves. It turns out that, depending on their speed c and the relation between the dispersion (i.e. the order of the pseudodifferential operator) and the nonlinearity, travelling waves maybe stable or unstable. Sharp conditions to that effect are given.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 3-4 , 1990 , pp. 195 - 212
Copyright
Copyright © Royal Society of Edinburgh 1990

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