Dynamic behaviors of soliton solutions for a three-coupled Lakshmanan–Porsezian–Daniel model

In this paper, we use the Riemann–Hilbert (RH) approach to examine integrable three-coupled Lakshmanan–Porsezian–Daniel (LPD) model, which describes dynamics of alpha helical protein with interspine coupling at fourth-order dispersion term. Through spectral analysis Lax pair, construct higher-order matrix RH problem for LPD when jump particular is a $$4\times 4$$ unit matrix, exact N-soliton solutions model can be exhibited. As special examples, also investigate nonlinear dynamical behaviors single-soliton, two-soliton, three-soliton and breather soliton solutions. Finally, an generalized N-component its linear discussed.