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Transactions of the American Mathematical Society

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Stability of multiple-pulse solutions

Author: Björn Sandstede
Journal: Trans. Amer. Math. Soc. 350 (1998), 429-472
MSC (1991): Primary 35B35, 58F14, 34C37
MathSciNet review: 1360230
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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

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