  Solitons and breathers are nonlinear modes that exist in a wide range of
physical systems. They are fundamental solutions of a number of nonlinear wave
evolution equations, including the uni-directional nonlinear Schr\"odinger
equation (NLSE). We report the observation of slanted solitons and breathers
propagating at an angle with respect to the direction of propagation of the
wave field. As the coherence is diagonal, the scale in the crest direction
becomes finite, consequently, a beam dynamics forms. Spatio-temporal
measurements of the water surface elevation are obtained by
stereo-reconstructing the positions of the floating markers placed on a regular
lattice and recorded with two synchronized high-speed cameras. Experimental
results, based on the predictions obtained from the (2D+1) hyperbolic NLSE
equation, are in excellent agreement with the theory. Our study proves the
existence of such unique and coherent wave packets and has serious implications
for practical applications in optical sciences and physical oceanography.
Moreover, unstable wave fields in this geometry may explain the formation of
directional large amplitude rogue waves with a finite crest length within a
wide range of nonlinear dispersive media, such as Bose-Einstein condensates,
plasma, hydrodynamics and optics.
