What is the expiation for a solemn oath, and does it differ from the expiation for an ordinary oath?

The expiation for a solemn oath is the same as the expiation for a non-solemn oath. A solemn oath is one that is made more serious by the time, such as swearing an oath after Asr prayer, especially on Friday Asr; or by the place, such as swearing an oath at the minbar of the congregational mosque from the direction of the mihrab, or between the Rukn and Maqam in Mecca; or by adding more of God's names and attributes; or in the presence of a gathering of prominent and righteous people from the town.