A pawn in superchess is defined as piece that only move forward and promotes to a promotion piece. By the way a king or emperor is a promotion piece :-)

normal pawn moves as in normal chess including en-passant

t-pawn moves one square forward or JUMPS two squares forward. It captures horizontal.

running pawn: This pawn has always the move possibility of two steps forward. It can also capture a piece that is two squares diagonal away. NO En-passant.

Mobilisation pawn: MMoves ones, two or three squares forward or captures one, two, three squares diagonal forward. No En-Passant. This pawn is a stock piece. It will never appear at a start positon. You can drop it on the first row (white row 1, black row 8) instead of a move.

Superpawn: Move as many psoobile squares forward or captures as many possible squares diagonal forward. No en-passant. I think that this pawn is stronger than a rook.

Note about promotion: The collection of promotion pieces contains ONLY the agreed pieces if they are captured and the removed normal chess piecers including the king if this pieces has been changed by the emperor. You cannot promote to Amazon, Grand Duke, Maharadja, Minister or General.