Riemann–Hilbert problem associated with the vector Lakshmanan–Porsezian–Daniel model in the birefringent optical fibers

Abstract

In this paper, we investigate vector Lakshmanan–Porsezian–Daniel (VLPD) model which can be used to describe the ultrashort pulses in the birefringent optical fiber. Based on the unified transformation method, the Riemann–Hilbert problem is introduced and initial‐boundary value problems of the VLPD model are studied. By solving the formulated matrix Riemann–Hilbert problem, the potential function solutions of the VLPD model can be reconstructed. Moreover, that the spectral functions are not independent but meet the so‐called global relation is shown.