  We propose a multi-component generalization of the modified short pulse (SP)
equation which was derived recently as a reduction of Feng's two-component SP
equation. Above all, we address the two-component system in depth. We obtain
the Lax pair, an infinite nember of conservation laws and multisoliton
solutions for the system, demonstrating its integrability. Subsequently, we
show that the two-component system exhibits cusp solitons and breathers for
which the detailed analysis is performed. Specifically, we explore the
interaction process of two cusp solitons and derive the formula for the phase
shift. While cusp solitons are singular solutions, smooth breather solutions
are shown to exist, provided that the parameters characterizing the solutions
satisfy certain condition. Last, we discuss the relation between the proposed
system and existing two-component SP equations.
