Matrix Spectral Problems and Integrability Aspects of the Błaszak-Marciniak Lattice Equations

Abstract

A method to derive the matrix spectral problems of the Blaszak–Marciniak lattice equations is proposed, and the matrix Lax representations of all the three-field and four-field Blaszak-Marciniak lattice equations are given explicitly. The integrability aspects of a three-field Blaszak–Marciniak lattice equation is studied as an example. To be specific, an integrable lattice hierarchy is constructed based on the matrix spectral problem of this lattice equation, the N-fold Darboux transformation and exact solutions are derived, the solitary wave structures and interaction behaviours of these exact solutions are displayed graphically, and finally the infinitely many conservation laws are listed in a standard way