Cauchy matrix structure and the (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa equation

Abstract This paper applies the Cauchy matrix approach to construct the (2 + 1)-dimensional Date-Jimbo-Kashiwara-Miwa (DJKM) equation with σ 2 = ± 1 and study its integrability. By imposing certain dispersion relations on r and s of the Sylvester equation KM + ML = rs T , the DJKM equation is established through equations of the master function S ( i , j ) = s T L j C ( I + MC ) −1 K i r . The connection of the τ function of the DJKM equation to Cauchy matrix approach is clarified. Moreover, Lax pair and exact solutions are derived for the DJKM equation systematically. It is interesting that the DJKM equation possesses diverse solutions. As examples, soliton solutions, breathers and interaction solutions are presented and illustrated under different choices of σ 2 = ± 1.