Cauchy matrix approach for H1 a equation in the torqued Adler–Bobenko–Suris lattice list

Abstract

As a torqued version of the lattice potential Korteweg–de Vries equation, the H1 ^a is an integrable nonsymmetric lattice equation with only one spacing parameter. In this paper, we present the Cauchy matrix scheme for this equation. Soliton solutions, Jordan-block solutions and soliton-Jordan-block mixed solutions are constructed by solving the determining equation set. All the obtained solutions have jumping property between constant values for fixed n and demonstrate periodic structure.