Initial–Boundary Value Problem for a Nonlinear Modified Boussinesq Equation

We study the problem with a homogeneous Neumann boundary condition and classicalinitial conditions for a modified Boussinesq equation. Based on the compactness method, it isshown that the approximate analytical solution constructed in the form of Galerkin’s sum over thesystem of eigenfunctions of the Neumann boundary value problem converges \(*\) -weakly to the exact solution.