Stability of multiple-pulse solutions

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 N -pulses bifurcating from a stable primary pulse. The system depends only on the particular bifurcation leading to the existence of the N 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 N -pulses bifurcate for any fixed N > 1 N>1 . Among them are infinitely many stable ones. In fact, any number of eigenvalues between 0 and N − 1 N-1 in the right half plane can be prescribed.