  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.
