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

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

2011-02-11

arxiv.org/abs/1102.2374v1

Nonlinear Sciences

Pattern Formation and Solitons

19 pages, 1 Figure, to appear in Nonlinearity

Scientific paper

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.

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