The Two‐Component Discrete KP Hierarchy

ABSTRACT The discrete KP hierarchy is also known as the th modified KP hierarchy. In this paper, we consider the corresponding two‐component generalization, known as the two‐component discrete KP (2dKP) hierarchy. First, starting from the bilinear equation of the 2dKP hierarchy, we derive the corresponding Lax equation by the Shiota method, which uses scalar Lax operators involving two difference operators, and . Then, starting from the 2dKP Lax equation, we obtain the corresponding bilinear equation, which includes the existence of the tau function. From the above discussions, we can determine which are essential in the 2dKP Lax formulation. Finally, we discuss the reduction of the 2dKP hierarchy corresponding to the loop algebra .