Specify direction of propagation in the 1-d wave equation in NSolve and NDSolve [duplicate]

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I am solving the 1-d wave equation with the following initial conditions:

weqn = D[u[t, x], {t, 2}] == D[u[t, x], {x, 2}];
icn = {u[0, x] == Cos[x], Derivative[1, 0][u][0, x] == 0};
DSolveValue[{weqn, icn}, u[t, x], {t, x}]

The solution, as expected, is simply

1/2 (Cos[t - x] + Cos[t + x])

It is well known that these two solutions correspond to waves propagating to the right and to the left, respectively.

Now I want to solve the same equation with the same b.c.

tmin = 0; tmax = 10; xmin = -15; xmax = 15;
NDSolve[{weqn, icn}, u, {t, tmin, tmax}, {x, xmin, xmax}]

Mathematica solves the equation and gives the following warning

Warning: an insufficient number of boundary conditions have been specified for the
direction of independent variable x. Artificial boundary effects may be present in
the solution

In this simple case, I know the analytical solution and can pick, say, the solution that represents the wave propagating to the right.

Is there any way to make Mathematica pick that particular solution?