STABILITY OF MULTIPLE-PULSE SOLUTIONS

In this article, stability of multiple-pulse solutions in semilinear p arabolic equations on the real line is studied. A system of equations is derived which determines stability of N-pulses bifurcating from a s table primary pulse. The system depends only on the particular bifurca tion leading to the existence of the N-pulses. As an example, existenc e and stability of multiple pulses are investigated if the primary pul se converges to a saddle-focus. It turns out that under suitable assum ptions-infinitely many N-pulses bifurcate for any fixed N > 1. Among t hem are infinitely many stable ones. In fact, any number of eigenvalue s between 0 and N - 1 in the right half plane can be prescribed.