i totally disagree, dover beach is indeed a monologue, yet not a dramatic monologue. the definition of a dramatic monologue is the kind spoken by someone else instead of the author, and in dover beach, arnold, the author IS the speaker
A dramatic monologue is spoken by a solo speaker, and it is addressed to a silent listener whose presence is felt. The speaker is usually in a state of some intense emotional crisis which initiates the speech that combines suspense and intensity of drama with the passion and melody of the lyric.
Arnold's poem Dover Beach is an elegy on the crumbling of faith in the industrialized and commercialized world of man. It is a solo speech that ventilates a deep sense of doubt and anguish, comparing the calmness of the Dover sea which is full to the brim and the receding 'sea of faith' from the shores of human habitation. The speaker addresses someone, presumably his beloved, as is evident in ' Come to the window'. The presence of the silent listener is also suggested at the beginning of the concluding verse--' Ah love, let us be true to one another'. A tormented individual speaking in the first person, a passive listener present throughout, a deep sense of crisis, and the blend of the dramatic and the lyrical make Arnold's poem a dramatic monologue.