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

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