Explicit solution and Darboux transformation for a new discrete integrable soliton hierarchy with 4x4 Lax pairs

摘要

The Darboux transformation method with 4x4 spectral problem has more complexity than 2x2 and 3x3 spectral problems. In this paper, we start from a new discrete spectral problem with a 4x4 Lax pairs and construct a lattice hierarchy by properly choosing an auxiliary spectral problem, which can be reduced to a new discrete soliton hierarchy. For the obtained lattice integrable coupling equation, we establish a Darboux transformation and apply the gauge transformation to a specific equation and then the explicit solutions of the lattice integrable coupling equation are obtained. Copyright (c) 2017 John Wiley & Sons, Ltd.