Stability of multiple-pulse solutions
- Sandstede, Björn
2010 Mathematics Subject Classification
- 35B35 35K55 34C37 37G99
- solitary waves, homoclinic orbits, semilinear parabolic equations on the real line, infinitely many N-pulses
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.
- Trans. Amer. Math. Soc., 350 (1998), pp. 429-472