Write a program that solves the equation in the discretization form using RK$4.$ Solve it in the region $10<=$ x $<=10$ with a grid size $$x $=0\mathrm{.}1,$ and use periodic boundary conditions: x$(10)=$ x$(10)(6)$

Integrate from t $=0$ to t $=2,$ using an appropriate time$-$step that satisfies the stability condition. For each of the initial conditions below, plot the solution at t $=2$ and comment on the results.