Inverse scattering transform for the coupled Lakshmanan-Porsezian-Daniel equation with nonzero boundary conditions

The challenge of solving the initial value problem for the coupled Lakshmanan Porsezian Daniel equation, while considering nonzero boundary conditions at infinity, is addressed through the development of a suitable inverse scattering transform. Analytical properties of the Jost eigenfunctions are examined, along with the analysis of scattering coefficient characteristics. This analysis leads to the derivation of additional auxiliary eigenfunctions necessary for the comprehensive investigation of the fundamental eigenfunctions. Two symmetry conditions are discussed to study the eigenfunctions and scattering coefficients. These symmetry results are utilized to rigorously define the discrete spectrum and ascertain the corresponding symmetries of scattering datas. The inverse scattering problem is formulated by the Riemann-Hilbert problem. Then we can derive the exact solutions by coupled Lakshmanan Porsezian Daniel equation, the novel soliton solutions are derived and examined in detail.