Inverse scattering transform for the coupled Lakshmanan–Porsezian–Daniel equations with non-zero boundary conditions in optical fiber communications

Abstract

The challenge of solving the initial value problem for the coupled Lakshmanan–Porsezian–Daniel equations which involves non-zero boundary conditions at infinity is addressed by 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 not only leads to the derivation of additional auxiliary eigenfunctions but also is necessary for a comprehensive investigation of the fundamental eigenfunctions. Two symmetry conditions are discussed for studying 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. Subsequently, we derive analytical solutions from the coupled Lakshmanan–Porsezian–Daniel equations with a detailed examination of the novel soliton solutions.