  A study of two-pion scattering for the isospin channels, $I=0$ and $I=2$,
using lattice QCD is presented. M\"obius domain wall fermions on top of the
Iwasaki-DSDR gauge action for gluons with periodic boundary conditions are used
for the lattice computations which are carried out on two ensembles of gauge
field configurations generated by the RBC and UKQCD collaborations with
physical masses, inverse lattice spacings of 1.023 and 1.378 GeV, and spatial
extents of $L=4.63$ and 4.58 fm, respectively. The all-to-all propagator method
is employed to compute a matrix of correlation functions of two-pion operators.
The generalized eigenvalue problem (GEVP) is solved for a matrix of correlation
functions to extract phase shifts with multiple states, two pions with a
non-zero relative momentum as well as two pions at rest. Our results for phase
shifts for both $I=0$ and $I=2$ channels are consistent with and the Roy
Equation and chiral perturbation theory, though at this preliminary stage our
errors for $I=0$ are large. An important outcome of this work is that we are
successful in extracting two-pion excited states, which are useful for studying
$K\to\pi\pi$ decay, on physical-mass ensembles using GEVP.
