Electron. J. Diff. Equ., Vol. 2009(2009), No. 158, pp. 1-20.

Stability of negative solitary waves

Henrik Kalisch, Nguyet Thanh Nguyen

Abstract:
The generalized regularized long-wave equation admits a family of negative solitary waves. We show that there is a critical wave speed dividing the range of stable and unstable negative solitary waves. Our proofs of stability and instability are based on a variant of the general theory by Grillakis, Shatah and Strauss.

Submitted February 17, 2009. Published December 11, 2009.
Math Subject Classifications: 35Q53, 37C75.
Key Words: Solitary waves; orbital stability; instability

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Henrik Kalisch
Department of Mathematics, University of Bergen
Johannes Brunsgate 12, 5008 Bergen, Norway
email: henrik.kalisch@math.uib.no
Nguyet Thanh Nguyen
Department of Mathematics, University of Bergen
Johannes Brunsgate 12, 5008 Bergen, Norway
email: nguyet.nguyen@math.uib.no

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