Lax pair in m × m matrix functions form of the m-component modified KP hierarchy

Abstract In this paper, the m-component modified KP hierarchy is introduced as an identity expressed in terms of free fermions and tau functions, where tau functions are defined as group <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>G</mml:mi> <mml:msub> <mml:mi>L</mml:mi> <mml:mrow> <mml:mi mathvariant="normal">∞</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> orbitals. Subsequently, the Hirota bilinear identity, which as a system of partial differential equations, is derived using simple lattice vertex algebra. Finally, we present the bilinear identity in the form of m × m matrix functions. Based on this, we obtain the wave operator, Sato equation, Lax equations, and other pseudo-differential operators in matrix form.