Eigenfunctions of the small oscillations about the double-sine-Gordon kink

We investigate the spectrum of the small oscillations about the $4\pi$ double-sine-Gordon kink. Our method makes use of the supersymmetry which naturally arises in any one-dimensional Schrödinger equation for which the ground-state wave function is exactly known. We provide for what we believe to be the first time analytical expressions for the unnormalized eigenfunctions of the internal and continum modes. Our result improves previous numerical investigations. Its relevance for the dynamics and thermodynamics of kinks is discussed.