• Media type: Text; Report; E-Book
  • Title: Stability of multiple-pulse solutions
  • Contributor: Sandstede, Björn [Author]
  • imprint: Weierstrass Institute for Applied Analysis and Stochastics publication server, 1995
  • Language: English
  • DOI: https://doi.org/10.20347/WIAS.PREPRINT.148
  • Keywords: 37G99 ; 35B35 ; 35K55 ; article ; 34C37 ; solitary waves -- homoclinic orbits -- semilinear parabolic equations on the real line -- infinitely many N-pulses
  • Origination:
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  • Description: 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.