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Stability of multiple-pulse solutions

Author(s): Björn Sandstede
Journal: Trans. Amer. Math. Soc. 350 (1998), 429-472.
MSC (1991): Primary 35B35, 58F14, 34C37
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Abstract: In this article, stability of multiple-pulse solutions in semilinear parabolic equations on the real line is studied. A system of equations is derived which determines stability of $N$-pulses bifurcating from a stable primary pulse. The system depends only on the particular bifurcation leading to the existence of the $N$-pulses.

As an example, existence and stability of multiple pulses are investigated if the primary pulse converges to a saddle-focus. It turns out that under suitable assumptions infinitely many $N$-pulses bifurcate for any fixed $N>1$. Among them are infinitely many stable ones. In fact, any number of eigenvalues between 0 and $N-1$ in the right half plane can be prescribed.

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Additional Information:

Björn Sandstede
Affiliation: Weierstraß-Institut für Angewandte Analysis und Stochastik, Mohrenstraße 39, 10117 Berlin, Germany
Address at time of publication: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210-1174
Email: sandstede@wias-berlin.de

DOI: 10.1090/S0002-9947-98-01673-0
PII: S 0002-9947(98)01673-0
Keywords: Partial differential equations, solitary waves, homoclinic orbits, stability
Received by editor(s): April 25, 1995
Received by editor(s) in revised form: September 19, 1995
Copyright of article: Copyright 1998, American Mathematical Society

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