Abstract
In this paper, we study a 6-field integrable lattice system, which, in some special cases, can be reduced to the self-dual network equation, the discrete second-order nonlinear Schrödinger equation and the relativistic Volterra lattice equation. With the help of the Lax pair, we construct infinitely many conservation laws and a new Darboux transformation for system. Exact solutions resulting from the obtained Darboux transformation are presented by using a given seed solution. Further, we generate the soliton solutions and plot the figures of one-soliton solutions with properly parameters.
Highlights
Dating back to the work of Fermi et al in the 1950s,1 nonlinear integrable lattice equations have been the focus of many nonlinear studies
We study a 6-field integrable lattice system, which, in some special cases, can be reduced to the self-dual network equation, the discrete second-order nonlinear Schrodinger equation and the relativistic Volterra lattice equation
The Volterra lattice and the modified Volterra lattice equation have recently been solved by Darboux transformation.[7,8]
Summary
Dating back to the work of Fermi et al in the 1950s,1 nonlinear integrable lattice equations have been the focus of many nonlinear studies. Sn,t = i(1 ± SnSn∗)(∓Rn∗+1 ± Rn∗ ), which is a special reduction of the four-field Ablowitz–Ladik equation,[2] and infinite conservation laws, N -fold Darboux transformation, N -soliton solutions of (3) were obtained in Ref. 19. Motivating by the above work, Zhu et al gave a simple approach to derive conservation laws for some semi-discrete systems from Lax pair directly.[22,30] Recently, Vakhnenko modified procedure of the recursive approach,[31,32] which is applicable for any semi-discrete integrable system associated with the auxiliary square spectral and evolution matrices of an arbitrary order. We point out that referring onto the already known general formulas for the collection of generating equations and the set of Riccati equation presented in Ref. 12, the hierarchy of infinite number of conservation laws for system (1) can be obtained. The infinite number of conservation laws (10) and (13) for system (1) satisfy the symmetry between the field variables pn zn, qn yn, rn xn
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