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