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Title: Stationary multi-kinks in the discrete sine-Gordon equation
Abstract We consider the existence and spectral stability of static multi-kink structures in the discrete sine-Gordon equation, as a representative example of the family of discrete Klein–Gordon models. The multi-kinks are constructed using Lin’s method from an alternating sequence of well-separated kink and antikink solutions. We then locate the point spectrum associated with these multi-kink solutions by reducing the spectral problem to a matrix equation. For an m -structure multi-kink, there will be m eigenvalues in the point spectrum near each eigenvalue of the primary kink, and, as long as the spectrum of the primary kink is imaginary, the spectrum of the multi-kink will be as well. We obtain analytic expressions for the eigenvalues of a multi-kink in terms of the eigenvalues and corresponding eigenfunctions of the primary kink, and these are in very good agreement with numerical results. We also perform numerical time-stepping experiments on perturbations of multi-kinks, and the outcomes of these simulations are interpreted using the spectral results.  more » « less
Award ID(s):
1840260 1809074
PAR ID:
10321326
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Nonlinearity
Volume:
35
Issue:
2
ISSN:
0951-7715
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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