WIAS Preprint No. 148, (1995)

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.

Appeared in

  • Trans. Amer. Math. Soc., 350 (1998), pp. 429-472

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