What is the significance of the songs in The Caucasian Chalk Circle?

Do you know the names of these particular songs. I've found the songs sung by Grusha, and another sung by Azdak, but I've found no songs related to Arkadi. Do you have any more details?

In the context of the play, they are all sung by the heroine, Grusha Vachnadze, a servant girl working in the governor’s kitchen at the time of a bloody coup. In the confusion, the murdered governor’s infant son is left behind by his horrible mother, who is more interested in which dresses she can save. The child is found and rescued by Grusha, who flees the city, hunted by soldiers who wish the child heir dead. Over the course of her travels and travails, Grusha falls in love with the child, finally claiming him as her own. The Song of the Rotten Bridge, Lullaby, and Song of the Child reflect a progression from her loving and claiming the child, to seeing in him a future of redemption for the sins of his father. In the second song, Song of the Center, Grusha sings of her fiancé Simon, who has been conscripted into the military to fend off the invading armies.

please give me the answer