The [formula omitted]-fold degenerate Darboux transformation of the three component Kundu–Eckhaus equations: Novel interactions between soliton and positon solution

Abstract

In this paper, an explicit representation of the N-fold degenerate Darboux transformation (DT) for the three component Kundu–Eckhaus equations, which can be viewed as a model to describe the effect of quintic nonlinearity on the ultra-short optical pulse propagation in non-Kerr media, has been derived. The DT is expressed by the initial eigenfunctions, spectral parameters and ‘seed’ solution. As applications of DT, the abundant and novel interactions between soliton and positon are discussed in detail, such as elastic interactions, inelastic interactions and bound states.