Numerical behaviour of the solution of the BGYB equations for a fluid-rigid wall system

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Abstract
The density profile is calculated for a Lennard-Jones fluid in contact with a rigid wall. The first member of the Born-Green-Yvon-Bogolyubov hierarchy of integral equations was solved numerically. The assumption was made that the two particle distribution function depends only upon interparticle distances. We used the pair correlation function for a homogeneous fluid obtained by molecular dynamics method. If the resulting non-linear integral equation is linearized, the Wiener-Hopf integral equation with a convolution kernel is obtained. The solution of this equation gives moderate agreement with the solution of the non-linear equation. We studied the criteria for the existence of the solution of the linearized integral equation. The existence of the solutions of non-linear equation was found to be closely related to the existence of the solution of the linear equation. Close to the liquid-solid line the solution diverged.