Stationary multi-kinks in the discrete sine-Gordon equation

We consider the existence and spectral stability of static multi-kink structures in discrete sine-Gordon equation, as a representative example family Klein-Gordon models. The multi-kinks are constructed using Lin's method from an alternating sequence well-separated kink antikink solutions. then locate point spectrum associated with these solutions by reducing problem to matrix equation. For $m$-structure multi-kink, there will be $m$ eigenvalues near each eigenvalue primary kink, and, long is imaginary, well. obtain analytic expressions for terms corresponding eigenfunctions very good agreement numerical results. also perform time-stepping experiments on perturbations multi-kinks, outcomes simulations interpreted