Stability of multiple-pulse solutions

Sandstede, Björn

doi:10.1090/S0002-9947-98-01673-0

Stability of multiple-pulse solutions
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Trans. Amer. Math. Soc. 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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