  Solitons are coherent structures that describe the nonlinear evolution of
wave localizations in hydrodynamics, optics, plasma and Bose-Einstein
condensates. While the Peregrine breather is known to amplify a single
localized perturbation of a carrier wave of finite amplitude by a factor of
three, there is a counterpart solution on zero background known as the
degenerate two-soliton which also leads to high amplitude maxima. In this
study, we report several observations of such multi-soliton with
doubly-localized peaks in a water wave flume. The data collected in this
experiment confirm the distinctive attainment of wave amplification by a factor
of two in good agreement with the dynamics of the nonlinear Schr\"odinger
equation solution. Advanced numerical simulations solving the problem of
nonlinear free water surface boundary conditions of an ideal fluid quantify the
physical limitations of the degenerate two-soliton in hydrodynamics.

Fluid Dynamics;Pattern Formation and Solitons