Abstract
It is shown that recent results on the stability of a double sine-Gordon soliton and its oscillation mode obtained by E. Majern\'{\i}kov\'a [Phys. Rev. E 49, 3360 (1994)] include some essential errors. In fact, static and moving kink-soliton solutions of this equation are stable for any positive value of the characteristic parameter \ensuremath{\lambda}. The oscillation mode for this kink does not show any instability for large \ensuremath{\lambda}.
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