Resumen de Studies on a Three-Field Lattice System: N-Fold Darboux Transformation, Conservation Laws and Analytic Solutions

Yuan Shen, Bo Tian, Dan-Yu Yang, Tian-Yu Zhou

• Researches on the nonlinear lattice equations are active, with the applications in nonlinear optics, condensed matter physics, plasma physics, etc. What we study in this paper is a three-field lattice system, which can be reduced to a modified Toda lattice system and a coupled lattice system. Based on a known Lax pair, we present an N-fold Darboux matrix, and then construct an N-fold Darboux transformation for that system, where N is a positive integer. The first three conservation laws of that system are determined via the Lax pair. Utilizing that N-fold Darboux transformation with N = 1 and 2, we obtain the one-fold solutions and two-fold solutions of that system. Those solutions can be used to describe the discrete solitons. Via the onefold solutions, we present a combination of the kink-shaped discrete one soliton and bell-shaped discrete one soliton. Amplitude, shape and velocity of that combination remain unchanged during the propagation.