Interaction of double sine-Gordon solitons with a space dependent potential wall as well as a potential well is investigated by employing an analytical model based on the collective coordinate approach. The potential is added to the model through a suitable nontrivial metric for the background spacetime. The model is able to predict most of the features of the soliton-potential interaction. It is shown that a soliton can pass through a potential barrier if its velocity is larger than a critical velocity which is a function of the initial soliton conditions and also characters of the potential. It is interesting that the solitons of the double sine-Gordon model can be trapped by a potential barrier and oscillate there. This situation is very important in applied physics. The soliton-well system is investigated by using the presented model. Analytical results are also compared with the results of the direct numerical solutions.

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