Fission and fusion interaction phenomena of the discrete kink multi-soliton solutions for the Chen–Lee–Liu lattice equation

Abstract

Chen–Lee–Liu (CLL) lattice equation is an integrable discretization of the CLL equation which can be used to model the evolution of the self-steepening optical pulses without self-phase modulation. In this paper, the discrete N-fold Darboux transformation (DT) is used to derive the discrete kink multi-soliton solutions in terms of determinant for CLL lattice equation. Soliton fission and fusion interaction structures of such solutions are shown graphically. The details of their evolution are investigated by using numerical simulations, showing that a small noise with amplitude less than or equal to 0.01 produces a strong oscillation and instability of these kink soliton solutions. The discrete generalized perturbation [Formula: see text]-fold DT is constructed to express some rational solutions in terms of the determinants of CLL lattice equation by modifying the discrete N-fold DT. Infinitely many conservation laws for CLL lattice equation are constructed based on its Lax representation. Results in this paper might be helpful for understanding the propagation of optical pulses.