Long-time asymptotics for the integrable nonlocal Lakshmanan-Porsezian-Daniel equation with decaying initial value problem

Abstract

In this work, we study the Cauchy problem of integrable nonlocal Lakshmanan-Porsezian-Daniel equation with rapid attenuation of initial data. The basis Riemann-Hilbert problem of integrable nonlocal Lakshmanan-Porsezian-Daniel equation is constructed from Lax pair. Using Deift-Zhou nonlinear steepest descent method, the explicit long-time asymptotic formula of integrable nonlocal Lakshmanan-Porsezian-Daniel equation is derived. For the integrable nonlocal Lakshmanan-Porsezian-Daniel equation, the asymptotic behavior is different from the local model, due to they have different symmetry for the scattering matrix. Besides, since the increase of real stationary phase points also makes the asymptotic behavior have more complex error term which has nine possibilities in our analysis.