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

Abstract

In this paper, we use the Riemann-Hilbert (RH) approach to examine the integrable three-coupled Lakshmanan-Porsezian-Daniel (LPD) model, which describe 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.

General multi-soliton and higher-order soliton solutions for a novel nonlocal Lakshmanan–Porsezian–Daniel equation

“…Proof. Begin from the first symmetry relation of Q, the anti-Hermitic symmetry (16). Take hermitian conjugate on both sides of the scattering Eq.…”

“…Due to the important application in nonlinear optics, abundant optical solitons [6][7][8][9][10][11] and some new exact solutions [12] for LPD equation were explored. Besides, the rich dynamic behaviors of solitons, rogue waves and the interactional solutions for a multi-component LPD equation were studied by Darboux transformation [13][14][15][16] and inverse scattering method [17].…”

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

“…23 In the past 10 years, the IBVPs and soliton solutions of many completely integrable models have been extensively studied. [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] As far as we know, the IPVBs of the VLPD model have not been studied. Therefore, in this paper, we will use the UT method to analyze the IBVPs of the VLPD model on the half-line domain (see Figure 1): Ω = {0 < z < ∞, 0 < t < T}.…”

“…In 2012, Lenells extended the UT method 22 and analyzed the IBVPs of the Degasperis–Procesi model with high‐order matrix Lax pairs 23 . In the past 10 years, the IBVPs and soliton solutions of many completely integrable models have been extensively studied 24–42 . As far as we know, the IPVBs of the VLPD model have not been studied.…”

Algebro-Geometric Solutions of a ( 2 + 1 )-Dimensional Integrable Equation Associated with the Ablowitz-Kaup-Newell-Segur Soliton Hierarchy

“…Many other techniques for finding exact solutions have been also discovered: inverse scattering theory, Darboux transformation, Riemann-Hilbert method, etc. Recently, more exact solutions of soliton equations are found [10][11][12][13], and more dynamic behaviors are studied [14][15][16].…”