On a coupled Kadomtsev–Petviashvili system associated with an elliptic curve

The coupled Kadomtsev–Petviashvili system associated with an elliptic curve, proposed by Date, Jimbo, and Miwa [J. Phys. Soc. Jpn., 52:766–771, 1983], is reinvestigated within the direct linearization framework, which provides us more insights into integrability of this model from perspective a general linear integral equation. As result, we successfully construct for not only Lax pair composed differential operators in 2 × matrix form but also multisoliton solutions phases parametrized points on curve. Dimensional reductions based linearization, to Korteweg–de Vries Boussinesq systems, are discussed. In addition, novel class obtained D ∞ $D_\infty$ -type equation nonzero constant background as by-product.