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

Abstract

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.

19 pages, 1 Figure, to appear in Nonlinearity

References in corpus (2)

• On the generation and the nonlinear dynamics of X-waves of the Schroedinger equation
• Spatiotemporal interaction of optical beams in bi-dispersive media

Cited by in corpus (3)

• Some special solutions to the Hyperbolic NLS equation
• WKB analysis of non-elliptic nonlinear Schrodinger equations
• Global Well-Posedness of 2D Non-Focusing Schrödinger Equations via Rigorous Modulation Approximation