In Arms and the Man, Raina's mother, Catherine, is in raptures at the supposedly daring cavalry charge Sergius (Raina's fiance) has just led against the Serbians. Raina is equally ecstatic that all her ideals regarding war and soldiering have been realized with this one heroic act of her fiance's. She tells her mother that she hasn't been without doubt herself, despite Sergius' bravery; after all, weren't all her ideals the inspired work of Pushkin and Byron?
In the play, Sergius' "half tragic, half ironic air,... mysterious moodiness" is reminiscent of Byron's Childe Harolde who "fascinated the grandmothers of his English contemporaries." Sergius is the perfect Byronic hero. He is equal parts cynical, moody, mercurial, sophisticated, intelligent, world-weary, mysterious, and above all else, unpredictable. Byronic heroes are radicals at heart; the tyrannies that encapsulate the status quo of their time often spark an answering cry of rebellion in the souls of these passionate men. So far, everything sounds good, right? So, why does Raina doubt her fiance?
One reason could be that the often emotional and unpredictable temperaments of Byronic heroes often hid personal weaknesses. The self-doubt, personal vanities, and private vices of these men often become their undoing despite their best intentions.
As for Pushkin, it was well known that he was greatly influenced by Byron; both were Romantics passionately moved by the social and political oppressions of their time. Pushkin's Eugene Onegin was the quintessential (pure and essential essence of something) Byronic hero. World weary and a bit of cynic, Onegin was also apathetic and self-centered. For the most part, his Byronic counterpart, Childe Harolde, was just as disillusioned and world-weary as Onegin. Both sought political and social change, yet both were tormented with inexpressible inner turmoil and conflict.
Juxtaposed against the sturdy pragmatism of Captain Bluntschli, Sergius's Byronic qualities eventually fail to sustain the interest of the secretly practical Raina. Yet Raina is not without her own ideals. Influenced by Verdi's Ernani, Raina shelters Captain Bluntschli, telling him that his safety is just as sacred to her as it was to the old Castilian noble who housed his enemy, Ernani, in his castle.
Hope this helps! Thanks for the question.