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In this note we propose a new set of coordinates to study the hyperbolic ornon-elliptic cubic nonlinear Schrodinger equation in two dimensions. Based onthese coordinates, we study the existence of bounded and continuoushyperbolically radial standing waves, as well as hyperbolically radialself-similar solutions. Many of the arguments can easily be adapted to moregeneral nonlinearities.

Radial standing and self-similar waves for the hyperbolic cubic NLS in 2D