It can be used. Follow these links to have an idea about numerical approach to solve any PDE.

http://math.stackexchange.com/questions/1341074/runge-kutta-method-for-pde

first equation has to solution and it has to be unique in tje domain so u can have numerical solution

Yes, it can be used to solve the PDEs in the sense of MOL. But in such a scenario, the system is often stiff and RK 23 is more appropriate than the ordinary RK4.

Yes, I think the equation can be solved using RK method. The idea is to apply Fourier transform w.r.t. space; doing this removes the derivative(w.r.t. x) terms and thus converts the system in the form of Y' = F(Y) which can be solved using RK method. 

Since the RK methods are derived on the first order ordinary differential equations, so can be solve it the higher order also, by making the linear system of first order ODE.

so if you get or could you drive with PDE by same technique for any independent variables, you can use to solve PDE, and the goal is how to find dependent variable.

yes, use shooting method and the resulting equation can be solved using Runge-kutta method

ytes first shooting hen runge kutte

You can use to solve PDE , the resulting equation may be solved after shooting method

You can check this article Rang Kutta used on PDE performance

Article Runge-Kutta Integration of the Equal Width Wave Equation Usi...

Abhijit Boruah

Firstly, you have to discretize the space of PDE (For example you can use finite difference (implicit or explicit) method for space), After that you have a system in ODEs then you can use runge-kutta method.

Rk can solve ordinary differential equation which need initial conditions; but pde are kined of boundary value problem, so you can not use rk to solve pde

You need to convert pde to a system of ode and to have the initial conditions

yes of coruse: Convert your system using finite difference method, so you will get a system of ODE

s, and then you can apply Rk4 to solve the system