Radial standing and self-similar waves for the hyperbolic cubic NLS in   2D
  In this note we propose a new set of coordinates to study the hyperbolic or non-elliptic cubic nonlinear Schrodinger equation in two dimensions. Based on these coordinates, we study the existence of bounded and continuous hyperbolically radial standing waves, as well as hyperbolically radial self-similar solutions. Many of the arguments can easily be adapted to more general nonlinearities. 
P.G. Kevrekidis, A.R. Nahmod and C. Zeng
nlin.PS math-ph math.AP math.MP