## Stability of multiple-pulse solutions

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**350**(1998), 429-472 Request permission

## 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
- ORCID: 0000-0002-5432-1235
- Email: sandstede@wias-berlin.de
- Received by editor(s): April 25, 1995
- Received by editor(s) in revised form: September 19, 1995
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**350**(1998), 429-472 - MSC (1991): Primary 35B35, 58F14, 34C37
- DOI: https://doi.org/10.1090/S0002-9947-98-01673-0
- MathSciNet review: 1360230