Analytic solutions of Hamilton-Jacobi equations

We establish the convergence of a modified variational iteration sequence to the local analytic solution of the Cauchy problem for Hamilton-Jacobi equations with analytic Hamiltonians and initial data. The main ingredient is the method of majorants. A significant finding is the precise estimation of the expansion of each iteration function, allowing the identification of an analytic majorant that majorizes all these functions near the origin. Finally, as an application, we give numerical results on how to use this method to approximate the analytic solution to the inviscid Burgers’ equation with quadratic monomial initial data.