Far-field asymptotics of the high-order solitons for Lakshmanan–Porsezian–Danie equation

Based on the generalized Darboux transformation, we construct high-order solitons for the Lakshmanan–Porsezian–Danie equation under the zero background. Then, we derive a Riemann–Hilbert problem for these high-order solitons. Using this Riemann–Hilbert problem, we find that when the variables (x, t) are proportional to the order n, we can analyze the large-order asymptotics. As the order increases, the (x, t) plane can be divided into four different asymptotic regions, which we refer to as the exponential-decay region, the algebraic-decay region, the genus-zero region, and the genus-one region. For each asymptotic region, we verify the consistency between the exact solution and the asymptotic solution.