Solitons 3 Two-dimensional Airy waves 1 Bending instability 1 Bose-Einstein condensation 1 Contour dynamics 1 Control nonlinearities 1 Dark solitons 1 Deepwater 1 Existence theory 1 Finite depth 1 Frequency components 1 Fundamental frequencies 1 Governing equations 1 Gravity-capillary solitary waves 1 Harmonic analysis 1 Harmonic generation 1 Harmonics generation 1 Localised 1 Localized solutions 1 Nonlinear equations 1 Nonlinear optics 1 Nonlinearity function 1 Quadratic nonlinearities 1 Second harmonics 1 Second-harmonic fields 1 Second-harmonic generation 1 Self-similar solution 1 Spatial solitons 1 Statistical mechanics 1