Stability of multiple-pulse solutions

Author:
Björn Sandstede

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

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Abstract | References | Similar Articles | Additional Information

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 -pulses bifurcating from a stable primary pulse. The system depends only on the particular bifurcation leading to the existence of the -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 -pulses bifurcate for any fixed . Among them are infinitely many stable ones. In fact, any number of eigenvalues between 0 and 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:
https://doi.org/10.1090/S0002-9947-98-01673-0

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

Article copyright:
© Copyright 1998
American Mathematical Society