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We report the theoretical derivation and the experimental as well asnumerical observation of nonlinear phase domain walls in weakly nonlinear deepwater surface gravity waves. The domain walls presented are connectinghomogeneous zones of weakly nonlinear plane Stokes waves of identical amplitudeand wave vector but differences in phase. By exploiting symmetrytransformations within the framework of the nonlinear Schr\"odinger equation wedemonstrate the existence of exact analytical solutions representing suchdomain walls in the weakly nonlinear limit. The walls are in general oblique tothe direction of the wavevector and stationary in moving reference frames.Experimental and numerical studies confirm and visualize the findings. Whiledomain walls are well known from many other fields in physics where strongnonlinearities are involved, e.g. in the case of dispersive shock waves, thepresent findings demonstrate that nonlinear domain walls do also exist in theweakly nonlinear regime of general systems exhibiting dispersive waves.

Phase domain walls in weakly nonlinear deep water surface gravity waves