Phase domain walls in weakly nonlinear deep water surface gravity waves

We report the theoretical derivation and the experimental as well as numerical observation of nonlinear phase domain walls in weakly nonlinear deep water surface gravity waves. The domain walls presented are connecting homogeneous zones of weakly nonlinear plane Stokes waves of identical amplitude and wave vector but differences in phase. By exploiting symmetry transformations within the framework of the nonlinear Schr\"odinger equation we demonstrate the existence of exact analytical solutions representing such domain walls in the weakly nonlinear limit. The walls are in general oblique to the direction of the wavevector and stationary in moving reference frames. Experimental and numerical studies confirm and visualize the findings. While domain walls are well known from many other fields in physics where strong nonlinearities are involved, e.g. in the case of dispersive shock waves, the present findings demonstrate that nonlinear domain walls do also exist in the weakly nonlinear regime of general systems exhibiting dispersive waves.