Long-time Asymptotics for the Reverse Space-time Nonlocal Hirota Equation with Decaying Initial Value Problem:without Solitons

In this work,we mainly consider the Cauchy problem for the reverse space-time nonlocal Hirota equation with the initial data rapidly decaying in the solitonless sector.Start from the Lax pair,we first construct the basis Riemann-Hilbert problem for the reverse space-time nonlocal Hirota equation.Furthermore,using the approach of Deift-Zhou nonlinear steepest descent,the explicit long-time asymptotics for the reverse space-time nonlocal Hirota is derived.For the reverse space-time nonlocal Hirota equation,since the symmetries of its scattering matrix are different with the local Hirota equation,the v(λ_(i))(i=0,1)would like to be imaginary,which results in theδ_(λi)^(0)contains an increasing t(±Imv(λ_(i)))/2,and then the asymptotic behavior for nonlocal Hirota equation becomes differently.